The noise is most likely conducting (through the wires) not transmitting (through the air). If it were your inverter it should still be audible with key on only.
You could have a bad RCA... or still have a ground loop.
With engine on and noise present check each chanel at the amp input for the injected noise by unplugging and listening for a change (noise gone/lowered). If it still makes noise with all RCAs unplugged then it's on the DC power side. If one RCA is mostly to blame try replacing it and do the test again.
Do the same test on the RCAs from carputer to head unit.
What type of ground loop isolator are we talking; how is it connected?
I found that my original ground loop was between the sound card (output ground was same as chassis ground) which was also head unit ground but not the same grounding points. I put isolation transformers inline on the RCAs and this cured the problem. But I didn't like the sound - too messy, as the transformers weren't the correct impedence. So I ended up with a 48 kHz fiber optic transfer and it's very clean - full volume engine running and not a peep of engine noise.
And I also run an inverter - there are other devices I plug in like external drive AC/DC supplies, drill, chargers etc.
Start here and let me/us know the results.