So I tried a few more things but I'm still getting the buzz/hum.
If you did so without talking to the manufacturer then you were wasting your time. This is a problem that has a very specific cause and I suspect that manufacturer, if a good one, would like to know about it.
I've encountered this problem before- as I mentioned in my prior post, its most likely a grounding problem, such as the controls themselves are insulated from the chassis since the chassis is finished with either paint or anodizing (both of which insulate). If the control bodies are not grounded they can pick up noise; when you touch them that noise pickup will be more obvious.
If the chassis is not properly grounded it can have the same effect. The chassis is supposed to be a safe harbor in which the audio circuit resides. If its not grounded, it can instead inject noise. Its worth getting this fixed.
Call the manufacturer (or dealer, if you can't contact the manufacturer)!