There is no way the galaxy can reserve engineer a reaper drive core in such a short time span since reaper core's "break the know laws of physics". The static discharge system was also designed for space stations not space faring ships since its akin to a lighting rod, which raises the question if the galaxy has managed to solved the issue of static then build up why isn't being used by all FTL capable ships? 2000+ years is more than enough time to make the technology more practical.
The galaxy has already reverse engineered Reaper tech. It isn't far-fetched at all as there is precedent for it in the lore. It is done with the thanix weapons, and you can use the Shadow Broker terminal to dispatch remote drones to salvage tech from a destroyed Reaper that can be used to give Shepard a stat boost. The terminal states that the drones allow the recovery of Reaper tech without exposure to indoctrination, so it was presumably how Sovereign's weapon was reverse engineered as well.
Reaper drive cores only seemed like magic because the galaxy had no working knowledge of what was going on inside a Reaper. It was a mystery because prior to the Reaper War the galaxy could only observe what was going on outside of a Reaper's hull, and Sovereign was so thoroughly demolished (presumably) that the debris wasn't sufficient. While the bit about Sovereign's debris is an assumption, I think it is plausible one. After all the Thanix is greatly inferior to a Reaper's main gun, despite being a knock off. The galaxy wasn't able to recreate it completely, which potentially lends some support for Sovereign being too destroyed for the engineers to truly get a working understanding of everything going on inside it.
That mystery of what is going on inside Reaper's should realistically end during the course of the Reaper War. There are multiple Reapers that are destroyed but still in an intact state. Drones poking around in the drive core would fill in the blanks for those mystified engineers, and Reaper propulsion would cease to be magic.
The Batarians also had something like twenty years to poke around an intact Reaper. While they had no idea what they had found and all ended up indoctrinated, it certainly possible that scans or technical specs from the engineers poking around the ship ended up in a Batarian state archive somewhere, and that those archives could be accessed by some who did not have personal exposure to the Leviathan of Dis. With the collapse of the Batarian Hegemony it isn't too far-fetched that a defector could have provided intel to the Council or the Alliance, or even that Spectres or Special Operatives raided Batarian intelligence during the course of the war. I kind of like the idea of a Batarian defector turning over specs to the Leviathan of Dis to the Council or the Alliance, since it would make that Batarian a hero and present a more balanced portrayal than the 'all humans are a blight!' types we usually ran into during the games.
There is nothing in the games that says the static discharge facilities of space stations can't be used for an ark. We don't know why they weren't use on ships. It is an assumption, and potentially a false onem that because it wasn't done, it can't. It could just be that wasn't cost effective for ships. Or that the facilities would need to be towed for a ship. Or that they simply were not necessary for any ship travelling within the galaxy. The writers have a completely blank slate to work with there, and they could port the tech to an ark without running into a single lore obstacle.