24 hybrids? Ouch.
Depending on how badly I wanted the system, I'd leave and come back later if the galaxy layout allows me otherwise I would emp the system and rush the command station.
The EMP would stun the hybrids fleets and 24 hybrids are not enough to stop a ship cap of fighter and bombers from popping the command station.
As soon as the command station dies, the hybrids should all run away, splitting up to different systems, so you can hunt them down later while they are in smaller groups.
Without using an emp missile? Keep throwing ships at them. Siege starships are very effective (used to be called dreadnaughts), but more on the bare hull after the hybrids force field is down though.
There are other options as well, but those are the first two that come to my mind.
D.