I wouldn't mind homogenizing the endings. I'd like to think that life isn't that much dependent on what Shepard and pals did, as long as the life continues at all. That could even be the point. Depends on if the places we already know about end up being isolated for so long time they evolve into each ending sporting their own galapagos syndrome, after nature being in different kind of contacts with syntetics - but are we even talking about that long time spans. I'd like the differences to be carefully considered and something that creep on you when you finally hear about them, moreso than everything looking different but being the same at heart. Anyway, this shouldn't necessarily be bigger task to pull off than with acknowledging previous games in ME3. Maybe. Milky Way's big, we don't need to visit every place and for example see geth with out own eyes aside few npc in Control and Synthesis. We already saw them enough, now let's head to Dekuuna and other new places.
I don't think Refuse needs to be addressed, probably neither do low EMS endings since people knew when playing how important that was. Though of course it's up to the players with low EMS to say how important it was for them! At least ignoring Refuse seems valid, you couldn't continue your game in ME3 either if Shepard didn't survive ME2 mission. (Many games have these optional bad endings.) What I think would be interesting is paragon and renegade differences in Control.
Choosing universal "canon" ending would mean erasing Shepard from the story of many players. In that case why should there need to be any connection to original games at all. Why (forced) canon state for one thing but not for everything else?
I'm not writing this because I think they should avoid moving to Andromeda. I'm going there full of curiosity. It's just that if there's gonna be references, or eventually a return in future title, it'd be nice to customize those references and hear about some outcomes and consequences.
Though I admit it would sound kinda fun if there was three direct sequels, or one with three different world states, for the same group of characters to go through. Story/stories would likely be shorter than in typical ME game, but if they're not that homogenized and new characters are charismatic enough, it sounds like fun to play through them all even if that means hearing about someone else's Shepards, and that game probably being a standalone.
I'd vote for homogenizing for time being or just fully moving on. Anything but prequels. Suikoden moved onto prequels after series original creator left... It was such interesting series, and suddenly a peek into the past felt somehow too safe and tired in comparison. In that case at least. Maybe it could work if the time skip was bigger (Suikoden game about ancient sindarin adventures wouldn't sound too boring because we don't know what happened to them, did their culture end for tragic and scary reasons or was it just some mundane progress), or if it's openly more lighthearted game from the start, a story about smaller scale adventurers who can't change the world but have fun and have to fight hard for their personally important reasons. Or The Sims In Citadel!