Bonus EXP doesn't sound like a very enticing reward, especially if the player lvl is capped; when I installed the SkilledUp mod, I jumped straight to lvl 126. Expanding on the descriptions of custom ships of the IBB bosses added in the Ships and Weapons Pack, I'd like to be able to customize ships myself:
E.g. I once defended my Starfortress against some Ordos and hadn't realized just how many joined the battle. I fought with a battle size of 200, and deploying a Victory Capital Ship instantly brought me down to -45 or so DP. When the thing reached single-digit CR and had like 5k integrity left, the REDACTED deployed their last Solar Capital Ship. My Starfortress was at ~40% integrity and only had its citadel and the two modules on either side of it left, I was tired and just wanted this to be over, so I increased battle size to 500 and deployed my three Paragons.
Afterwards, I realized I had destroyed 139 REDACTED ships in the battle, 9 of which were Capitals and I think about 130 or so saw their end when the only thing I had deployed was my Victory. What I'd like to do here is slap the title of "Defender of <colony-name>" onto that Victory, give it a paintjob, increase its OP and maaaybe increase the size of two weapon mounts. You could do a similar thing to the AI ships, where a Pirate Atlas Mk. II, that has participated in three successful attacks on Orbital Stations, becomes something like the "Scourge of Askonia" or wherever the attacks took place.
To add a disadvantage, if you have several ships with the title "Defender of <Hegemony-Colony/System>" in your fleet and the faction of the system you jump into is currently hostile with the Hegemony, you could be denied access to the port of a planet. Plus if your fleet is made up of several custom ships that have seen dozens of battles and all carry distinguishing names, it'd of course be harder to hide your identity with your transponder turned off. To expand on the "Contacts", destroying a unique ship - even if it is a Pirate - could anger other captains because they have fought besides the captain of the destroyed ship in the past.
Something else I wouldn't mind seeing is "actually designated crew". At the moment, if you place a few ships in storage because you want to screw around, you may run into the problem that you have to "put some crew / marines into storage", too. I guess you could split "crew" into "normal workers", which are used to e.g. colonize a planet, and "ship crew", which is obviously used on ships. If you put a ship into storage, you'd then either leave the crew of that ship on it, or you'd get those guys and gals back into the available pool of crew for your ships.
If the crew is deployed in a battle, they'd gain experience and a more experience crew raises certain stats of the ship. However thinking about things like "crew becoming experts on a ship when they're employed on there for a long time", makes me think tracking several thousand crew members' deployment history may go a bit overboard. However coming back to that point of making risky fights more desireable, you could make it harder and harder for a crew to gain exp, to the point they'd have to destroy half the opposing fleet by themselves in a battle, effectively making the player think of deploying another ship as "deploying kill stealers".
Plus with "designated crew", losing a ship in a battle would actually hurt. At the moment, you lose a ship in battle and say "Eh, I have like 5 more of those back at base" or you can just buy another one over at that station. Well OK thinking about that I guess people would be more likely to just deploy as many ships as possible so they don't lose that one ship which has a veteran crew and three titles from previous endeavours, but hey it's a singleplayer game and you can just reload.