Could you post a save? That really helps more than any amount of text description.Under the textbox when posting, click Additional Options ==> Attach ==> Browse (select your save).
(Oh, and no warheads. 10/10.)
Just from the text, you are describing a perfect use case for warheads. Not nukes, just a couple lightning IIIs to severly damage or kill the guardians/starships. If you are playing FS, you should be able to deal with the AIP.
If you remain unwilling to do that, I would recommend using riot starships+champion shields+shield bearers to grab the fleetships back to the chop-shop, then send some cloaked unit way away from the threatball, and pounce with your whole fleet when the threat strings itself out trying to pursue.
If you really feel like cranking out the cheese, use a combination of snipers, transports, and cloaker starships. Once the snipers fire a couple volleys from the system edge, retreat them into the cloaked transports, wait for the threat to return to its original position, repeat.
All this is assuming you don't have golems, spirecraft, or k.
Edit: Thanks, I'll look into it, should post within 1/2 an hour with some semblance of a solution.
Edit2: You have martyrs (in raw xampite form). Use them. You may want to follow up with rams, but those guardians are the main strength of the threatball, so your fleet should take care of the golems by itself.
I may have to bill you for a melted computer.