Sounds a bit like this: https://forum.ih8mud.com/100-series-cruisers/344210-exhaust-booming-idle.html
Part of the resolution in the TSB is replacing the engine mounts. I believe it calls for softer ones in the TSB, but if yours are just shot, then new regular ones should suffice.
I did a bunch of research on this issue when I looked at an '06 I considered buying that had a bit of the bass at idle in gear. Actually, my '07 has it slightly too, it goes away when the A/C compressor kicks on.
That's funny yours goes away when compressor on... it must just be a resonant frequency. Makes me feel better that it's probably not the compressor. It's definitely coming from inside the engine bay. I might have to get new motor mounts and see what happens. I would think I'd have vibration issues under load as well if it were motor mount. Maybe the buzzing at idle is just an early warning sign?
Utahfj62, did you have to lift the engine to get the mounts out?