This should not happen. There's nearly 2000 strength worth of Fortified Tesla Guardians, Plasma Guardians, and Concussion Guardians.
All they do is sit there. My entire fleet of 30 strength lasts about 15 seconds and can take out ONE stack, which the AI gets to rebuild in about 20 seconds (there are 3 instigators on that planet, THREE, two of which spawn 2.5% of a wave worth of units every 20 seconds). The planet is basically untouchable.
I was able to take out the AIP instigator and the command station (which, as it turns out, was irrelevant: the ships still sit there, the instigators still produce 2.5% of a wave every 20 seconds, and nothing's changed). But with that planet in on one side, a 116 strength nanocaust planet on the other (with 2 gravity guardians sitting on the wormhole) my only other option is to try and come around from the third (and last) wormhole I control.