To bounce off of OPs bit about trading the ships back to the original faction and your point about actually claiming such ships being tricky due to springing players forward... you could actually have a little feature here that could really change the way the game plays (at least for the way I play).
Take OPs scenario where a military Alliance ship is killed by pirates and the ship is abandoned. Perhaps you could either choose to scrap it all as you would now - OR - give an option to offer it back to the original faction for a substantial (but more easily managed to avoid breaking gameplay) reward. With a catch.
You'd have to wait X number of days for that faction to send a crew to reclaim it, and each day provides X% chance of more pirates coming that you need to fend off. Jumping away would immediately abandon your offer/reward.
At the moment my gameplay largely consists of jump in - mine/scrap a derelict ship asap and then jump away again to keep hu...