OK, so I just read the entire Ark Theory thread. There were some good points made about feasibility of intergalactic travel and the Ark Theory in general.
1) Discharging drive cores. Heimdall suggested the ships to carry some sort of ballast for that purpose, but I don't think it'll work since ballast will make the ships heavier and larger drive cores will be required, which, in turn, will force the ships to discharge cores more frequently. There is also the matter of costs for all that eezo, the trade of which is monitored. A way was suggested to reverse-engineer Reaper drive cores, but besides Sovereign there is only one Reaper before ME3, that derelict one which has its core intact. Of course, writers can come up with "they found another derelict Reaper" but I think it is going to be akin to the Crucible plans on Mars - too convenient. And Prothean technology is highly regulated. The penalties for withholding Prothean technology are some of the harshest in the galaxy.
2) Synthetics vs organics. Regardless of what you think about the endings, Bioware clearly believes the story they have told, about the conflict being inevitable. Thus, solving it plays a large role in the universe. Moving away to another galaxy before the endings does not remove the conflict. The only way I see for the Andromeda scenario to work alongside the resolution of this conflict is by making the Milky Way face an existential threat and force the races of the galaxy to move elsewhere. The timeline will probably be centuries away from the Reaper War.
3) Secrecy. It is suggested that the project is conducted in secrecy for quite a long time, before even ME1 events. However, the project will require large funding, access to ship-building facilities and brilliant scientists. If that group knows about the Reapers and believes their threat enough to pull such resources into the project, why don't they warn the others? They'll probably have a proof, solid enough that they spend that much money on the project. More, their existence is never mentioned in the trilogy, even in Shadow Broker intel and Spectre terminal.
4) Connection to Milky Way. Assuming the ships departed during Mass Effect 3 and centuries had passed, won't anyone be interested to find out what happened? The idea was presented that the colonists might not want to do that not to reveal their presence to the Reapers, but what of the people of Milky Way? Is it really plausible that nobody will find out about such a project after centuries from the Reaper War. It should be noted that the Protheans too had stored a message about their contingency plan in the beacons.
I also found it interesting that I've seen the names of some members who were quite opposed to the idea in that thread back then but argued for it in the recent discussions 
It's too late here (around 4 AM lol) and I'm probably forgetting a few points but those seemed quite major.
Personally, I believe that Bioware's best course of action is to set the game in an uncharted region of Milky Way and establish a basis for the move to Andromeda from that region.
Or have ships that flee from the final battle to be swallowed by a wormhole to Andromeda. It will also have the possibility to have a bunch of races in ME:Next that no one will bother to take to the ark ship - Batarians and Geth/Quarians (all based on the choices prior to the endings). The announcement of Orbit seems to indicate that there will be some form of Mass Effect: Keep (Arc?) to address those major choices. And even without the Keep they can add a bunch of races for this setup without invalidating player choices. Batarians and Quarian exiles can come from the Terminus fleet, Krogan too, Humans, Asari, Turians and Salarians are already there, Elcor and Volus too... Hell, we don't know anything about the Crucible wave, for all we know, the creation of wormholes can be a side effect from it and the Normandy is crashed in Andromeda 