Tactics and Tips *SPOILERS*

That's strange. I've lost escorting ships sometimes in that mission but I never lost the Invincible.

That reminds me to give another pro tip:
If you have an escort list (the small list of own or enemy ships on the right side of your screen that shows their hull status) in the mission you are playing, you can use the 'E' key to cycle through the ships in the list. And if you press 'G' while having a ship selected you target a ship that is attacking it. Combined that means you can attack those friggin' Paktahns who try to kill your carrier!
I don't know if that will help you though.
And yes, the Invincible is supposed to run and to survive in that mission IIRC. You are supposed to defend her.

I suppose you know it by now but I'll say it anyway: I hate such missions. Starting way back in 1990 with Enyo 2 in WC1.
It does seems like as I go along, the orders become a bit less clear, and the objectives a little more...free form. The price of success, I guess: no one's holding my hand anymore. When I'm defending the T'lan Meth jump point, I do get a sort of Behemoth-y feel to it. Those ships jump in faster than they can be destroyed. I've tried calling in the bombers and capship missiles as soon as they let me; I've tried waiting on the strikes, and I've tried doing one right away, then waiting on the other. I've targeted the Frathra II's launcher as soon as it jumps in, I've also ignored it and gone after bombers. Still ordered to retreat
I've even just ignored the retreat order, and hung around blasting capships as the fighters all go after the retreating Confed fighters. I actually destroyed every ship that jumped in, including the Wrathgar (two hours later. You think the rage would wear off at some point, but, no)

I feel a bit stuck. I don't mind losing, but I would like to at least know if I can win...
You should retreat when you get the order to do so. You cannot win that battle. Actually I thought some of the ships were even invulnerable in order to not allow the player to accidentally break the mission.
You can save the Invincible though. I'm not sure about the escorts, I think you will lose at least some of them.
At any point, can you kill Deathfang? It seems like I might've had the chance in the mission where you're supposed to protect the Bradshaw, but the lowest I could get him to was 27% before he cloaked. I want him dead soooooooo bad. And the Wrathgar (btw, you're right the Wrathgar is indestructible at the T'lan Meth jump point. Got carried away). I want it dead, too.
Well, since this thread carries the SPOILER tag anyway:
Remember that the major task of that huge Terran fleet is to lure the Kilrathi away and do as much damage as possible so Blair and the Victory can attack Kilrah. That is the main point of the last part of the story.

So yes, Deathfang will buy it, and so will the Wrathgar.

Deathfang and the Wrathgar are "recurring villains", which is the reason why you can't kill them until the plot has advanced far enough.
So, long time...doing a replay. Found a list of all the achievements and medals you can get, and am on Hyperion 2, trying to keep the Hermes' health above 89% (it's one of the bonus goals). It looks like that means it can't take even one torpedo. I've flown it (and reflown it) several times, and can't seem to keep ALL the torps away. Anyone had any luck with doing that...?