Honestly It's been a while since I read the Codex about space travel in Mass Effect so I don't remember it that much. But my view that the galaxy doesn't have the technology has to do with my view that developing a giant vessel capable of doing that travel is another scale of challenge than building the ships we see in the trilogy. So I can't argue this points much. But what about fuel?
Regardless, if we just consider the discharge issue. If we consider that they solved that problem, why wasn't it made common knowledge? That technology would greatly improve ships. Keeping it in secret seems... unproductive.
Further, the technology is not only about the Ark. The Tempest seems more advanced than the Normandy, so are the "Kodiaks" we see.
Not to mention, do you really think that the best answer to a future war is to built Arks instead of improving your military? It doesn't make any sense. If you have a way to solve the discharge problem, why wouldn't you equip your at least your military crafts with it, for example.
Regarding discharge, the fact that this option exists on space stations means that there are ways to manage the problem,
they are simply not efficient if your craft is not huge. Again, transferring the charge through some complicated system back into
the power plant seems not too far fetched.
And for all we know this technology isn't a secret, it's merely irrelevant due to size and complexity of the systems needed to eliminate the discharge.
Regarding re-fueling on the way, there are factors that make this problem slightly less crucial:
First, if needed the Arks could possibly spend most of the trip on a ballistic trajectory once they reach a sufficiently high top speed.
That would cut substantially on the amount of power needed, since the engines won't have to be active.
And as for the drive cores, even if you still need to maintain a mass effect bubble around the vehicle due to various FTL risks,
the power draw should be manageable assuming you have access to fusion technology and perhaps some rogue planets or other bodies to
stop by on the way and refuel.
Finally, if this is an act of desperation, they can always use riskier sources of fuel, like dark matter for example.
(should be easier for their technology, what's with their mastery of dark energy)
Regarding the logic of investing in such a plan instead of in improvement of military power, there could be multiple reasons.
Perhaps they reached a plateau of technology, perhaps the needed funds to significantly improve the military power of the citadel were much bigger
than this investment, perhaps they actually did both.
Or maybe they only had plans on "paper" in case of a true emergency, perhaps the Reaper attack on the citadel at the end of ME1 has shaken the council
much more than they admitted, and have decided to reactivate those plans.
There are many possibilities and speculations for everyone...