rocket and missile projectiles have an upgradeable hull strength statistic when you buy them for your ship...
meaning that each projectile can withstand so much damage before its destruction.
they start at 25 hit points and they do not have shields.
now, the blue hexagonal weapon ports will target incoming projectiles automatically... so you can use the bolter, gatling and laser weapon, but if you look at their starting hull damage stats (10, 6, 5, respectively) the best bet is the bolter, and it would still need to hit a missle or rocket 3 times to destroy it, which isn't likely to happen.
so, you upgrade their hull damage stat... the bolter with one hull damage upgrade outputs 15 damage, which would kill a missile/rocket projectile in 2 hits...
you have to upgrade the gatling and laser's hull damage twice to get it down to 2 hit projectile kills...
it's even better if you have a carrier, and you upgrade your fleet's hull damage, as they can often land a few hits on a projectile, or sacrifice themselves to block it entirely.
beyond that, it's all about how you orient your ship... using a ship with 2 hex bays on one side, both armed with bolters with upgraded hull damage, you just have to watch where the enemy is going, and keep that side pointed at the origin of enemy missiles.
as for getting slaughtered in the last sector, your best bet is to use a beacon to draw some of them out so you can take them on in smaller batches... waiting turns on the map screen can make a huge difference for you, use it strategically.
