You can also use an USB sound card, there's no need for a HAT/GPIO solution. Any card that advertises Linux support should work.
For a HAT solution, I think any of the DACs sold by the RPI folks directly might fit the bill - see https://www.raspberrypi.com/products/.

@dookieshooter I don't have a lot of programming/code experience to help people here, but I do have a fair amount of audio expertise and this is a fairly simple issue to solve. It's called an "audio ground loop" and it's because the audio signal isn't grounded to the same ground as the rest of your components. Perhaps it's plugged into a different outlet or surge protector. The reason your second amp worked is because it probably has a ground loop filter built-in and the first one didn't. The easiest and cheapest way to minimize or get rid of the hum is to buy a Pyle PHE300 or similar device that (depending on the model) either connects to the signal that's going to the speakers or to the audio OUT from the Pi. It intercepts the signal and 'cleans' the hum from it by grounding the signal again.

@mrnoholster Cool. As a courtesy for other users may I ask you to edit your heading of the post and add [Solved] or something similar, thanks.

The audio jack is not grade A at any Pi I own, so I moved to USB-audio, but good to know that HDMI with dedicated audio outlet does also work well.

One solution to noise and ground loops is to use an isolated sound card for the Pi.

If the sound card is magnetically isolated, then noise and hum (ground loops) from the Pi can't get to the acoustic pathway.

Matt

Try adding the following parameters in the /boot/config.txt file

disable_audio_dither=1 audio_pwm_mode=2

then reboot and see if it makes a difference.

Wow, It's been a while... So thanks for your answers: I will park my 'dedicated DAC' idea and simply pull the audio from the HDMI!