First off, I like your hypothesis PhantomRUS9! Especially the Arkships being a last ditch effort to survive.
I've got my own hypothesis (more of what I want to happen in the NME series, which I have 0% hope it will) if you'd like to hear it!
Going off of your Arkships as a last resort, during the events of ME3 the council comes up with a plan to send Arkships to Andromeda in case Shepard fails. They will put all those into stasis/cryo and send them on a journey that will take a LONG time. The explorers primary objective is to colonize Andromeda... but a select few undertaking the journey have a secondary objective. On the assumption that Shepard fails and the cycle continues, the secondary objective is for the colonists to develop or acquire advanced technology in the hopes of one day returning to the Milky Way and stopping the cycle.
During colonization of Andromeda, your protagonist stumbles upon the Remnant, an ancient and powerful race with very advanced technology. Throughout the series your protagonist tries to harness this technology as well as colonize Andromeda. Eventually your protagonist stumbles upon a great discovery, the Remnant had built a device similar to a wormhole that can send ships or people through space and time. Your protagonist uses this, with other remnant technology, to travel back to the Milky Way around the time of the Reaper attack on Earth. Your protagonist, combined with Shepard's efforts, defeats the reapers in a bloody battle for earth without the use of the crucible.
Again, this is what I would want to happen. Solely because then you'd have a happy ending all around and then Bioware wouldn't have to avoid the whole 'ending' fiasco, which would allow them to make games based in the Milky Way post-reapers.
Like/ dislike?
And yes, the ending of ME3 still gets to me :P
Tl;Dr: In NME series your character uses remnant technology to travel back to Milky Way and beat the Reapers.