Forget if I mentioned this, but I did play a short campaign with the Infection mechanics grafted onto a modernized Mouse Guard… and I don’t recommend it unless you understand all of the mechanics (e.g. how they behave in the long term) much better than I do!
I think Mouse Guard conflict would work just fine as is for dogfights; you’re not so much simulating the dogfight as you are the tactical level of the battle. You’re not attacking the enemy or defending yourself so much as you are attacking the enemy’s plans and protecting your own or your side’s assets. Raptors can ‘attack’ just fine at this level, as enemy ships are always a threat to your plans. (For all the enemy knows, they might be carrying missiles, preparing for a boarding action, laying down heavy ECM, etc.) Defending can be as simple as flying away from enemy ships, shooting down Cylon fighters near the BSG, etc.
The constant pressures in BSG were resources running out (which just gets worse as time goes on, minus the weapons depot), the proximity of the Cylons (which acts as a brake on the community or individuals to develop themselves, as they’re always on the run), the state of repair of the ships, the morale of the crew and civilians. Much or all of this you can do just fine without a specific mechanic.
There is something that might be of use, the so-called sociometric cycle, which is a way of mapping the lifecycle of enthusiasm and conflict in relationships onto the seasons. In Spring, we get excited about new possibilities, morale is up, infatuation, we start big new projects. In summer, things start to stretch; we’re overcommitted, differences in vision are revealed, resentments start to creep in. In Autumn, the conflict is open, and remains until something fundamentally changes. Winter is about solace and revisioning, finding guidance and the new direction to take.
So, one idea is to apply this to the survivors’ community as a backdrop to the players’ actions. In Spring, supplies are good - the ship is making strides towards Earth, moving on supply depots, holding elections, etc. In Summer, politicians are struggling to keep their promises, unpopular trade-offs are made, opposition factions are getting busy, cults are fomenting discontent. In Autumn, there’s outright war between factions; power is wrested from the leaders; riots; shootings - culminating in a coup or election that kicks things along for another cycle. (If you were true to the sociometric cycle, you’d skip winter completely, reflecting the fact that the community is under such pressure that it can never ‘find itself’ and take a sane step, and instead lurches from infatuation to infatuation, bold idea to bold idea.)
The obstacles that drive the calendar along might be Cylon raids, which have a much greater or lesser severity depending on the state of the community. Cylon attacks in Spring might be tough, but the CAP is ready, the community is behind them, etc. In Autumn, Cylon attacks are devastating; opportunist civilian captains use the attacks to make gains of their own, jumping away.
All this is assuming that the players are largely concerned with military actions outside the ship, or at the very least within the confines of the military hierarchy. If the players are mixing it up in the drama within the community, pushing for particular candidates, etc. then I think it would make more sense to have the state of the community reflect the challenge needs of the players rather than driven along a clock of their own. (And you might be wise to consider stock BE instead of MG.)
Another way entirely (or on top of this) would be to give the fleet itself (or just the Battlestar, or just the military vessels) Conditions. The state of the BSG could be a big factor in the humans’ disposition in space battles; the BSG itself could even be a ‘player’ in the Conflicts, taking on Attack actions with its massive guns, Maneuvering out of the way, Feinting to lure the Cylon Battlestars into exposed positions. Being Low of Ammo or Damaged could affect its abilities enormously.