Hard(er)core FTL: repairing breaches, doors or equipment costs scrap. The oxygen generator uses up fuel at a slow rate.
Edit: actually, no, that's simply harder FTL.
Hardcore FTL: each of your crewmembers have specific attributes and training, prior to you acquiring them, which dictates how good they initially are at doing certain tasks (piloting, shield operation, etc.) These skills can be improved over time. Crewmembers don't have hitpoints, instead they suffer bodypart-specific damage (semi DF-like). Your engineer loses a hand? Prepare for his/her engineering to be impacted accordingly. Your medic loses a leg? They're not going to crawl away from that airlock quick enough. Also, atmospheric simulation is improved - breaches or suddenly-opened airlocks will cause air in accessible compartments to flood outwards, dragging objects and people with it. Also, detailed diplomacy - you can negotiate your way past some encounters, but make an enemy in an early sector and let the ship/crew escape and, who knows, they might come after you later on. Your ship has fuel tanks, which can be targeted and can explode (if containing fuel), damaging nearby other compartments. Individual systems have individual wiring (to either your engine or a generator-type compartment), which can be damaged in combat and need to be fixed accordingly. Crewmembers can electrocute themselves if unprepared/unskilled. Asteroids can be mined for scrap (or other), but this takes time and needs to be done by crewmembers by hand (you're not flying a mining vessel, remember?), with all associated risks/rewards. The time pressure from the oncoming rebel fleet isn't as immediate, and you can perform slightly wider/better scans of your local systems, but the difficulty curve moves upwards to accommodate (so you need to work on improving your ship/crew more, rather than purely being able to/having to trust to luck).
Ship customisation (beyond simple binary "does this compartment exist here yes/no") would also be an option.
Edit 2: also, why only the one ship? If I cause another ship to surrender/kill all its crew, and I've got enough crewmembers to spare, why can't I captain one ship while having another following me in support? Hell, if the rebels can have a fleet/armada then so can I! Of course, maybe the crewmember I've given control of the other ship to might not like me as much as I think. Crew personalities could come into play. Perhaps they'll abandon me...or turn on me...at a critical moment. Hmm. Might be best to blast them out of the stars first. Or make sure I'm in the stronger of my ships. Just in case.