For posterity, I was able to fix my A30 Pro and I'm using it daily for a couple of weeks now.
Sadly I didn't take any pictures, but maybe this information will be useful for someone.
Under the heatsink there are two identical circuits, one for each channel. In the initial filter/regulator stage, there is one primary ceramic capacitor, connected to large L-shape copper traces, before the signal then goes to the Op-Amps.
In my case, the left capacitor was shorted. I desoldered the working capacitor on the right and measured around 20uF, typical values for 0805 ceramic capacitors are 15uF or 22uF, so I went with 22uF on both sides.
The main circuit runs on 25V, so I went for 0805 22uF 25V ceramic capacitors, as I couldn't find any higher rated ones with that specification anyways. There is little room under the heatsink. There are double stacked 22uF for 50V, but they would not fit.
After soldering and re-assembly, the relay clicking was gone. I tested it with disposable headphones for around 8h before plugging in my regular headphones.
If you attempt this, you should be comfortable with 0805 SMD soldering. It's your own risk, I'm just a guy on the internet without a schematic. Also, your device could have a different fault, I measured every component for shorts and only had one bad component.
