Re-establishing connection with the MW galaxy

I'm sure they won't have to pick an ending, as 600 years is a lot of time. It would be 2786, after all! In fact, I think all the endings work in a cascading order of consequences:

Control: The least change. The Reapers eventually leave.

Destroy: We lose the synthetics, but they probably rise again.

Synthesis: That's trickier, but we actually don't see what is the major consequences of the synthesis besides a few green eyes. They could downplay the consequences to a level that it isn't so different from other endings, aside from the loss of diference between what is a synthetic and what is an organic. Or we just get there anyway, eventually.

Refusal: Trickier, and one I wouldn't count as an ending, so much as a fancier game over like Joker's ending in Mass Effect 2. Anyway, still possible in 600 years, I guess. Scorched Earth. Just that it might not have been by the Reapers.

I might be misremembering stuff from the endings, of course.

Just out of curiosity, do we know the range of a mass relay? Would they have to setup multiple relays along the path, or just have a pair of them: one in Andromeda, one in the Milky Way?

Maybe.  Cerberus had it but the Alliance didn't seem to have it until they got their hands on the SR2.  That is, the Alliance STOLE the tech from Cerberus and installed it in their ships.  The AI was long gone before any of the Council races had that tech.

Honestly, if BioWare did commit to an ending, I'd probably be fine with it. However, Synthesis would be made pointless as an ending since the synthesized beings would be in contact with organics and synthetics. They would probably see them as enemies since they represent a known threat and the promise of the Catalyst that the synthetic/organic war would continue. Synthesis ending would probably result in a war with Andromeda if a connection was established.

Establishing contact with the Refusal ending brings the Reapers into Andromeda. I don't think anyone wants that.

It'd have to be Destroy or Control (doesn't need to be stated which). Details unnecessary. As Arcian said, "the Reapers were defeated" would suffice.

Okay if they reconnected with the milky way it really wouldn't matter which ending was chosen because it would be six hundred years in the future. The only problems I could see would be with the geth and quarian outcome and the krogan genophage being cured or not. It would have been at least six centuries away when our group links up with the milky way. With the exception of liara and wrex pretty much none of our squadmates would still be alive and the universe would have moved on. And they could easily say that the krogan natuarly overcame the genophage like they were doing before mordin remade it. I am not gonna get into each ending but they could easily have just a few sentences about different things. I do think the quarians and geth would have to be cannon or something which wouldn't be a huge deal to me. The green eyes in the one ending would have faded and they could say the reapers could easily be avoided by just not mentioning them. Six hundred years would be more then enough time for the decisions to blend together enough