Basically, the SI (a Concordat adventurer with the memories of someone from our universe from 2015), get access to the usual datacores - Helm, New Dallas - creates a decent mercenary unit (based on the CYOA rules) with some SLDF Royal tech.
Started to uplift the Concordat. At the time of the HBS game, helped Kame take power and later married her.
The Concordat participated in the Audurien Crisis on the side of the MoC, capturing some CC worlds.
Because of the knowledge of the SI the Concordat gets access to interesting toys, like an HPG and HPG tech, the hardware of the Argo, but not the dropship. Politically, with the removal of the most 'crazy' anti-Davion members from the ruling of the Concordat, the TC is much saner, and Edward starts a de-frozen with the FS and later FC.
The Reach is absorbed by the TC, specifically, with the Arano family in control of the now Aurigan province.
HPG tech is shared with the FC, and the following crisis with Comstar lead to a civil war on Earth, with the proto WoB (without the experience of Tukayyid) going for the FWL, while Earth turns independent - no sane C*.
The clans invade later because of no Outbound Light incident.
At that time, all the IS nations already had warships - some recovered some new and tech-wise are SLDF and moving for Royal level.
FWL has a nasty civil war and fragments.
SJ are destroyed and JF expelled.
The Reach is not only part of the TC but with a modern industry - same for the rest TC, mostly thanks to the efforts of the SI.
The TC is allied with the DC against the clans - don't like the ex-SLDF and can't see an alliance with the FC.
You know that in the vast Univers of Battletech such iterative approach is a wishfull thinking? Especially the uplift part? Becouse even over three decades is too small amount of time for the IS to modernise, given their force and power structure? And especially massive overburdened supply chains?
The same goes for warship production becouse even in your scenario by the time of the Clan Invasion you will have at best single digits of prototypes being tested. The domino progress and enlightment theory spreading from Aurigan Reach is not valid becouse the moment they start reorganising and building power, and note they have potential, they will suffer fate of modern Syria becouse they are a destabilising factor IF they allign with one of the neigbouring superpower. In reality scenario end here with similar way as Afghanistan in 1980s - after long time of courting with developement aids by the rival powers, one will invade either openly as humanitarian intervention or peacekeeping when some kind representatives of "Aurigan Alliance" materialise asking for brotherly help or we go good old way of financing expats who have lost power and wealth due to the ongoing changes, which given that Aurigan Reach is
de facto a feudal confederation, is more easier. Going the HBS 'verse story or not, that is the outcome, becouse the interstellar strategy and political background is already stacked against any possibility of independent and strong Arano ruled state. Also of note that Aurigan conflict might escalate with standard pattern for conflicts on the borders of sphere of influence. Especially with that local Lostech cache, which might not only lead to the direct intervention of the superpowers but also will likely end with intervention of the Comstar.
Even assuming that will not happen, and we will take a route of you secenrio, we came to the problem of technological spread and modernisation effort.
Battletech universe is not technologically primitive per se - their main problem comes from political power structure and supply chains.
Power structure is feudal, with most models of governance are feudal confederations, with most potent powers havin more centralised structure and greater power of the sovereign.
Supply chain problem steams from centuries of unrestricted warfare, which brings us to the state of broken back theory of warfare. IS and other polities do not actually have problem with hardware nor actually production capability - problem lays in their production, transport and maintanace capabilities which are permamently overburdened and backlogged, especially in case of high-tech components, that is why most of the IS line troops were so much way back technologically and doctrinally behind the Clans and couldn't stop their advance. The same goes for the supply and maintanenece of the civilian infrastructure, becouse of the demand exceeding orders of magnitude production capabilities, not mentioning the transport bottlenecks, all of that in the region of 2 million star systems. Modernisation would include creation from ground up whole new supply chains, science, education, laws, which will all need to be fed with the same amount of resources that barely are sufficient for supplying and maintaining current status. In best case scenario you will end with overtly developed to the level of IS Aurigan reach and spilling that to the periphery of your patron, rest are island and point developements.
Then we came to the military power - IS is mainly aero-mechanised military, with mechs as support or breaking force. Due to the supply and transport bottlenecks and the political power structure, IS powers have relatively small surplus of military power for offensive operations. Each large scale war that came into being was an effect of accumulation of necessary suprlus military capacity - hard to achieve in the broken backed world of Battletech, whcih needs to put considerable garrison forces and supporting them QRF/rapid deployment - 'verse is a universe of permament warlordism, feudal rivalisation and permament subterfuge and subliminal warfare (ie. so called hybrid warfare) - everytime you have large scale conflict or any emergency that eats on your limited military surplus, you are subjected to the chain rebellions, coups and actvation of local warlords, external raids from rival powers and mercenary warfare. Also contrary to the Clans, IS is the ones who are more ritualised at conduct of warfare, due to the delicate balance of power and broken backed world.
In case of Clans, they are mainly mech centered space-mechanised force, due to their numbers and avaiable military technology. Fact that they have managed to for a cohesive politically force and form interstellar invasion which managed to overrun major powers is only a testament to their capabilities. Given their growth enviroment, Clans are more "service guaranees citizenship" model of army society rather than tribal warrior culture. Also they are alone at that time who have real space power with institutional knowledge, interstellar power projection capability and modern, net-centric doctrine, which they use for deadly efficiency. These combined, plus their own history of internal warfare is centered on swift, precision strikes on chosen targets - Clans in war look more or less like SOFs storming building, and on that they excell, not some kind of one-on-one duels. Contrary to the IS, they have relative lack of institutional experiance for waging interstellar campaings, but given the lack of serious opposition at the begining, they will gain it during practice.
Also of note, invasion will be planned. Intelligence, reserves, deep space FOBs forming supply corridors, some cheap spinal modular cargo ships and all that. Also given their doctrine and size, main operating unit of Clan will be an all army independent strike force, which is maximising striking power and self sufficiency. You will have a pinpoint strikes with overwhelming space and air support with drops conducted right on the top of the enemies positions, supported with deep strikes on enemy's C4ISR, supply and communication hubs - BT 'verse does not have "fixed" interstellar routes - jump drives allow for conducting front-less war in whole volume of the operational theathre, and with their space fleet and experiance with using it, they have massive advantage.
It is going to be a return to the full scale, unrestricted warfare. Especially in yours scenario - Clans will be invading with force of greater cohesion with better prepared supply and reserve capabilities and also much more strike force and deep strike oriented doctrine. With IS escalating to the use of nuclear ordinance, all bets are off and we go back to the early Succession Wars unrestricted level of warfare, which will actually benefit Clans more - first they have much greater fleet and institutional knowledge of using it, two have secured industrial base outside the IS reach. Also such scenario will take place mainly in the captured territorry, which encompasess Periphery, which is a place that is treaded by the IS powers as an unrestriced proxy wars site and free fire zones. Arrival of the Clans preaching that they came to restore peace and order, manifesting with pacification of local warlords and stopping meddling of IS, then being subjected to the unrestriced IS raids against Clan FOBs will turn them to the Clanners side, who will gain not only local supprot in form of local basing and supply, but also will gain jannisaries who will make up for the lack of numbers. Also nuclearisation of the conflict will band Clans together becouse now the Clans will be facing (by the way together with Periphery states and populations of conquered territories) a genocidal crusade, a crusade that will mainly take place inside their own and Periphery territories. Also of note is a collapse of o supply chains and convinient FOBs for IS forces due to the previous Clan raids, making power projection to the Clan controlled zone much more difficult.
Also of note is the loss of the mentioned before surplus military capacity which will weaken postition of central sovereings. Copuled with internal dissent, propaganda warfare, mutual distrust and internal disslusionement with new war, and fact that there is an alternative for the feudal reality of IS, mainly Clan meritorcracy, IS will be forced to turn more and more forces and means to the internal stabilisation. With Clan expansion and IS crusade ground to halt due to the exhaustion and overextension, conflict will freeze and we will come to the old an beloved by the IS mercenary and hybrid warfare.
Also with modernisation of the IS and Comstar tech sharing we get a Jihaad.
In no scenario you will have an uniformed SLDF tech IS - only islandisation and more choked supply chains with Clans arriving later with better prepared, more cohesive invasion force, for the new threat, and even more guided by the first strike paradgim - countering imminent future IS invasion of Clans.
Of note is that the new Clan doctrine will look more like "evaluate and strike first" and IS would be "total defense" turning later to the conventional "Search and Destroy".
Also that should be useful as a planning tool.