How about this; DC Comics has separated all of their lengthy continuities into separate Earths. Every time someone comes up with a new, closed continuity, they just add another Earth with a number (Earth 2 or Earth 76).
Why don't we just start something similar with Star Trek? Right now we would have Trekverse 1 and Trekverse 2, but over time (maybe when Trek has entered it's 3rd re-imagining) it'll catch on.
You know, on thinking it over, I think something like this could be viable. We've already got "Prime Universe" for the original 1964-2005 continuity, and "prime" means "first." So we could have the Prime Universe and the Second Universe. I think that has a certain elegance to it. Or maybe Prime History and Second History, which is also kind of cool. And of course it could be extended to Third, Fourth, etc.