The fact that this cycle was able to do it in such a short time span yet past cycle and the reaper's weren't able to do it only serves to make the whole thing contrived. Its well known that past cycle's and the reaper's are subject to the same technological limitations as this cycle so this cycle should be treated no differently than the other ones.
If they want to reverse engineer one they first have to understand how the thing works in the first place and if they can't fully understand how it works then they can't reverse engineer it. Unlike the crucible they have no blueprints as to how to build one so they'll have to make one from scratch which will make the process more time consuming.
We don't know that other species never tried their own version of the ark project.
Again, the Council species don't understand Reaper drive cores only because they've never been inside a Reaper. That potentially changes during the Reaper War, and we don't know what role (if any) either the Leviathans or Batarians play. The Leviathans invented Reaper tech and the Batarians had twenty years to poke around the Leviathan of Dis.
We also don't know how often the ship would need to refuel. Dark space is in fact is a bit of a misnomer, as the space between galaxies is littered with stars. In fact as many half of all stars in the universe may lie between galaxies rather than within them. Since we don't know how often an ark would need to refuel, the writers could have an ark zig-zag between these intergalactic stars on its way to Andromeda, using the stars themselves for energy or topping off on orbiting gas giants.
In short, there's no reason why the writers wouldn't be able to get Milky Way colonists to Andromeda without resorting to retcons or contrivances. It's entirely possible to craft a reasonable enough explanation using the series own lore.
The bartarians aren't one who like to share their secrets so don't expect them to share their research anytime soon especially if they are the first to the reaper's.
The Reaper War is a little late to be holding on to secrets, particularly in the wake of the Batarian Hegemony's demise. A Batarian scientist or military or government official turning refugee and delivering information to the Council would be far from implausible, particularly when remnants of the Batarian fleet are part of the galactic alliance.
We know that the crucible alone is enough to bankrupt the entire galaxy and that's not even taking into account the war effort. If the crucible alone is enough to bankrupt the galaxy then there is no way the galaxy can support another large scale project like an ark ship.
We don't know that.
There is a Volus report on the galactic economy that Shepard can access from the Spectre terminal, but it never states that the Crucible alone was bankrupting the galaxy. It states that if the war continues along current projections that the galactic economy would go belly up within the year. It was referring to the entire economy and not a single slice of the Council's war budget.
Also if Bioware makes a Reaper War ark project the means of getting to Andromeda (not guaranteed, but a safe bet), that Volus report is obviously including the Ark project as part of its projections.