Except that the galaxies resulting from each ending are vastly different, by taking place in those galaxies, it concerns them. The only way the new story could take place in the same Galaxy is if all the endings, defying all logic, have the same long term result.
There is no need to address them, that's the point of the ark theory, NOT to trash the endings. If you want to trash them, then homogenize them or canonize one as you've been suggesting, that's the surest way to do it and make sure nobody's choice mattered to the fate of the Galaxy, since the same thing was going to happen anyway.
I see it exactly opposite. The way for the new story taking place after all three RGB endings is if the major differences are in the long-term.
You took destroy and the catalyst is right that this will lead to another organic vs. synthetic conflict? Alright, but with every synthetic in the galaxy destroyed, this will take time. 1000 years? 5000? 20000? I don't know, but it'll take time, because there are no synthetics to fight with at the moment.
You took control and worry that the Reapers could be back some day, because someone could take the power from catalyst-Shep? Might be the case, but nobody knows that Shep took over control and is behind the Reapers retreating. So someone has to find out about that and then find the new catalyst first and then find a way to take the power. Took "our cycle" 50000 years, so there might be time for the same conflict as after the destroy ending before we come to that.
You took synthesis and ... sorry, I don't even know what might happen after synthesis. So if it were me at the helm of ME, I would probably let this ending out going forward. I would ask the synthesis pickers if it would be OK for them if I tell them that "you did good, son (or daughter), you did good". If you take refuse, you lose, if you take control or synthesis new conflicts arise and if you take synthesis, you win. No more conflict. 
But let's assume for a second, that having won ME3 won't satisfy synthesis pickers. What's holding back the writers to put the same conflict after that ending that the galaxy might see next after the destroy and control endings?
Aight, so if we have established that the same conflict can happen after all endings, then the differences really only amount into what I have tried to tell you multiple times: the Geth/Quarian conflict and the genophage only mean that these themes won't have major differences on the main plot in the next game. And why should they? They were part of three games, so that should be enough. The Krogan might make a power play some day in the future or they might not - doesn't matter for the next story.
Picking different endings can be reflected in the next game by a lot of cool things: you sided with the Geth and didn't take destroy? Cool, here is your Geth squadmate. You... well, the rest isn't even having any major impact on the next game. Whether you helped the Krogan or not, there will be Krogan; same goes for the Quarian even if you sided with the Geth though their numbers might be very low (people, let go of the thought that the Quarians go extinct - they are spread all over the galaxy, so losing a war with the Geth doesn't mean that). But where is the problem anyways? I mean that are decisions you make in ME3, so maybe if you sided with the Geth you don't even want to see a Quarian in MEnext? If you took destroy you might be cool with not having a Geth squadmate because, you know, you thought destroy was necessary no matter the cost.
So I really don't understand why anyone would want to leave the galaxy behind and abandon the ME universe. Why? There is no reason to do it, other than not accepting the endings to ME3 - but they happened. They are part of the history in the ME universe and now the next part gets written.