Alrighty then. Assuming the battle has no other surprises, I've done the GM's work for the battle for him.
If we retreat now, we lose our shipyard, and they only lose swarmlings. We'd need to immediately research anti-swarm weaponry, then spend a few turns building those weapons, before we could get back in track for building larger ships. We likely won't have time to get defenses on a second planet before enemy reinforcements arrive.
If we refuse to just give up and let them kill the shipyard, while throwing the sacrifices already made in this battle away, we could try this: Move the ships up and fire at different swarms, fire one warden shot at each swarm.
If they commit all their carriers, and they have at least 7 attack, then we only have a 25% chance of keeping our shipyard intact, but we kill everything they've sent. If they commit 2 carriers, we have an even 50% odds. If they commit 1, 68.75% odds. If they commit none, 81.25% odds.
Things might work better if we reserve some Wardens for anti-ravager duties, but I don't feel like running through another one of those right now.
The above assume that partial swarmer stacks can merge with each other. If not, things get easier, as they have tiny swarmer groups getting in the way and not killing our Defenders.
I think three Defenders is an acceptable price to pay to kill this fleet and possibly save the shipyard. (If they don't send in their other ships, we can easily guard the shipyard, and will be in a much better position should they have replacement swarmers they can use again next turn) We can replace ships far more easily than they can right now, and being able to build dedicated space-faring vessels is critical if we want to do more than just bunker up on our home-world.
Edit: I like that idea, firing at ravagers. If they both die, we might only lose a single Defender this next round.
Action proposal is to move the Defenders up to a line along I-11, I-13, I-15. Each shoots the swarm to its upper right. As shown.
Four Wardens each fire at a swarm along H.
Two Wardens are on standby for Ravagers. If Ravagers don't enter their range, try for the carriers, or, failing that, the rear-most swarms.