Why does the game just have to be a future in the same universe? Imagine if the quarians just took off in their spaceships and kept going. How would the reapers find them at all? This kinda' ties in with my problem with the first game's plot. The logistics of taking out a spacefaring race. How can the reapers be sure they got everyone? The protheans somehow hid an entire planet from them and Javiik's hide away was found but they were too lazy to double check and he survived.
So what if a group got together before the war and decided they wanted to map out areas that aren't connect to mass relays yet? This group builds a massive space station and then the war breaks out. Alien races of all kinds want to escape so they join up with this group which takes off in the giant fleet to parts unknow. Maybe some quarians want to join them and since Shepard saved the geth, they have an A.I. in their suit. There are some krogains aboard too, seeing as how Shepard cured them they can repopulate in this new galaxy. Or maybe they all died.
Since they got the hell out of dodge before starchild, they don't have green eyes, don't have to worry about Shepard's reapers, and the geth can be alive with the reapers being dead as well