Long range and healing beams? In my eyes, that'd not even be necessary. If FCs would be destructible, even a mediocre pilot like me could take them down easily. With what I already learned in Wing Commander, decades ago. And it would even be easier here than in that game.
For the few not knowing how we destroyed capital ships in Wing Commander: you boosted behind the ship, through it's defensive fire. Placed yourself right behind that ship, where its turrets had a blind spot, stayed there and kept firing till it blew up. Now looking at the details:
- FCs won't shoot at you, unless you already attacked it. So if you are not an complete moron and already shoot from a distance, you can just easily fly there and get into position.
- In Wing Commander the things were sprites and in effect a box. Fleet Carriers actually have geometry.
- In Wing Commander you had to -guess- how the ship moved, due to the low quality of the sprites. In ED you can easily see how it moves. But you don't even need to, because:
- Fleet Carriers in ED actually have geometry. With spots where you can squeeze in and stay and no turret ever can reach you.
- Additionally, some of these spots even provide good cover from other ships.
So really, all it would take to destroy a fleet carrier is to go to solo, leisurely fly around it, park in one of the blind spots, which also provides plenty of cover from any potential escort and keep firing till it blows up. And there's really only a few "cures" for that:
- Invisible walls around big parts of the ship, so you can't exploit its geometry. Would be funny at least.
- Turrets placed inside all those spots. We'd win a reward for the spaceship with the most ridiculous turret mounts, for sure.
- Carriers shooting at every commander but the owner. That kind of defeats the whole "can be placed for business" idea, though.
- Carriers have a "blacklist" of people to shoot at. Think about it for a moment, what a can of worms that is. Enjoy.

- The carrier having so strong shield and/or hull regeneration that you can't destroy it that way. But then, that's just another flavor of indestructible, not worth the effort.
And only after that it's even worth pondering the crazy stuff from engineers.
Give it 100 km range and make any hit by them insta-kill. As long as it'll not be surrounded by invisible walls, will be the same shape as it currently is and won't be transformed into a globe with turrets around it, it won't make any difference.