I didn't see any opposition to that idea, and I'd like to move forward on it now, but figured I'd prompt some final bit of discussion before I put up a PR.
The only straightforward way to handle it that I see right now would be to add a last-turn-combat gate to the portion of Ship::Resupply() that handles updating current meter to max meter for capacity and secondary stat part meters. Weapon damage, Fighter count and bay launch rate are capacity type meters, weapon rate of fire (think flak) and fighter damage are secondary stat meters, it looks to me.
Although I do kind of enjoy being able to have my weapon damage upgrade while I am fighting Maintenance Ships, I'd be fine with all of those upgrades being gated by combat. What do you guys think?