He mentioned starting a new save and just moving over the ship files already
You know what, could be a corrupted settings file for a mod. I've had similar problems when some mod makes an "invisible window" on the screen, a region of the screen where if my mouse goes over it the input is locked as if a pop-up was there. I've think it's KER that does it, but I'm not sure. Resetting window positions on mods could help (see which mods have either settings on the stock toolbar or the advanced settings menu, and if any of them has some sort of "reset window positions" button you can access).
Other than that, all I can think of is trying all the mods. I've done it before on a game with some 70+ mods, it was boring as heck but it worked at least. The way I did it is this:
create two "quarantine" folders somewhere outside GameData, one for "testing" mods and another for "OK" ones.
Move half your mods to the "test" folder.
Check the mods that are left, if any of them requires a mod you just quarantined. If so, quarantine them, too.
Open KSP, see if problem persists.
If problem persists, problematic mod is still installed. Move the mods from the "test" to the "OK" folder, and repeat 2-4
If game works fine, then problematic mod is in "testing" folder. Repeat the process, but now add those mods back to the game.
Finally, when you found the guilty one, move everything from the "OK" folder back to GameData and see if it indeed does work.
If you find a more efficient workflow, I'd like to know!