I think it's more probable that they will find some kind of remnant tech that allows for faster travel.
Either some kind of relay like thing or faster / better ship drives that they manage to adapt to our ships.
They aren't going to force a canon ME3 ending- it just won't happen. It would create too much of a *-storm for starters which would be more detrimental to the games than anything else they could do to them.
If, I stress if, because I don’t think it will ever happen. If the milky way is ever revisited, they will either find a way to adapt all possible endings (even the cycle continues - could have been hidden pockets of milkyway species to return after the reapers are gone) or, they will do some kind of alternate universe.
600 years into the future - Sheps dead anyways no matter what ending you picked. The others could have died too for any number of reasons even the long lived species. It'd only take a question to the player about what ending they picked and a line or two of dialogue to sort it.
Our games now tho are andromeda and I expect the further into andromeda we get the more disconnected we will be from the milkyway.