What's the optimal way of doing this? I have zero trouble shredding the Gaitori and only taking one gunship pulse in the process, but the Salrillian carrier is an unholy beast to fight. That damn turreted beam makes the concussion missiles (!!!!!! unguided!) totally useless and it outranges the Fullerene Pulse Gun. How are on earth you are supposed to take that thing on with 3 ships and no stealth? Is there some maneuver I can do that will just occupy its attention until after the liner clears the system?

You need to do well against the Gaitori in order to have a chance against the Salrilians, but if you can keep it to one or two atomic pulses, you should be OK. It's true that the trans-space bolt renders your missiles unable to hit the carrier, but keep in mind that, so long as the bolt is busy intercepting your missiles, it can't hit you. If you get into mid-range (close enough to got the carrier, but far enough that the missiles stay in flight a couple of seconds) you should be able to destroy the carrier.

By the way, I believe it's possible to retarget the HVCs to follow you instead of the tug. If the Salrilians target the jumpgate instead of the tug, they can make a useful meat shield along the same lines.

My strategy is similar to Pallas Athene's except that I order the cruisers to attack the carrier directly and follow them in as closely as I can. Then I unload everything I have at the carrier at medium range, completely ignoring everything else. This is usually enough to shred it in about ten seconds. I find it best to withdraw to the tug afterwards to recharge shields a bit before continuing the fight.

Regarding the Gaitori: I've found that if you sit right on top of the jumpgate, you can usually destroy the gunship before it has a chance to fire. It takes a bit of practice but makes the fight against the Salrilians just that little bit easier.

I always send the cruisers to attack the Sal Carier. They draw fire and allow me to kill the carrier.
Then I hang around at the jump gate blasting away at everything.
I find that I seldom can fight the tug through unless I have secured the jump gate.

Occasionally the carrier will go after the tug or the disabled ship.
Sometimes the Carrier's escorting cruisers will go after them, so you need to watch out for this.
Very occasionally the Sal carrier never comes out of warp when the cruisers chase it

Fighting the Gaitori is a matter of practice. I seldom if ever get hit by them now. Your missiles can intercept and take out the Gaitori gunship pulse if it gets a shot off.