If they had years or decades to research it, I would agree. But they don't have years or decades, they have weeks or months to get a hold of a working core, study it until they understand it fully, reverse-engineer it to something they can use, putting it into a ship that has to be retrofitted for intergalactic travel, and leave in a manner of months. No technological advancement in Mass Effect's lore has done that much that fast, and that was with simpler things.
I'm arguing that a Reaper core can't be reverse-engineered and the resulting product being used for intergalactic travel in a manner of months, something that has never happened in the lore.
Thanix weapons and repurposed Reaper parts for the Crucible occurred within similar time constraints. On what basis is the Reaper core more complex and incomprehensible than these other parts that were copied or salvaged and reused?
If Bioware wanted to have the Council races reverse engineer or repurpose a Reaper core there are no lore roadblocks for doing so. No retconning is necessary as it has already been done in the series, and whether or not it is possible with the core as well is entirely up to the writers.
You can use a Reaper core, sure. But that provides more problems than solutions, like essentially just giving the Reaper a new body or the crew being indoctrinated.
Why was no one indoctrinated with the Thanix or Crucible projects? Both projects went off without a hitch despite using Reaper technology, when it would have been within the Reapers' best interests to prevent both from coming to fruition. If any indoctrination occurred, and given the success of both projects it seems that was not the case, it wasn't sufficient to derail either project.
Why should an ark project be any different?
Yes I am. Achieving interstellar travel and achieving intergalactic travel are already different scales of technological advancement. Especially when the former was spoon fed to the people while the latter has to be figured out from scratch by themselves and both being done in the same timeframe.
The comparison is quite frankly insulting to the latter scenario. It's like saying someone learning how to build a bike with detailed instructions next to it is an equal technological leap to someone learning how to build a spaceship from scratch. The difference is that big.
You say I'm grasping at straws, but in truth it is you and the others supporting the notion that are grasping at straws so it can work.
The only things preventing the Council races from travelling to Andromeda are the need to refuel or discharge drives and the time it would take to complete the journey. The last of those however is no real obstacle when the galaxy might be desperate for any means to ensure the survival of the space faring species. if spending 500+ years in cryosleep (or 230, if they can match a Reaper's speed) is what is necessary to ensure that, I doubt the Council species would hesitate. For the Asari or Krogan the time span isn't even that much of a burden as they can live for over 1000 years even without taking a Javik nap.
As for the need to discharge drives or refuel, while obstacles...they shouldn't be bigger hurdles for the Council species than the one faced by humanity before it had mastered FTL travel. I think declaring the elimination of drive discharge or finding a more effecient power source more of a challenge than FTL travei is arbitrary, not supported by anything in the games at this point, and underestimates, even with the introduction of EEZO and the mass effect, what a monumental achievement creating technology enabling FTL travel would be. If humanity can derive from 50,000 year old Prothean tech buried in Martian sand the ability to leave its solar system behind, it should also be capable of figuring out how the Reapers avoid drive discharge or refueling, provided it is the relevant tech to study.
You are indeed grasping at straws.
You'd be better off arguing why the ark setting would make for a less interesting story than whatever your preference is, than by trying and failing to argue that previously established lore says it absolutely can't be done. Because no such lore exists.