Thanks for the suggestions/help!
I checked/compared all pots and pots + their accompanying resistor combinations and all gave the same results, so it seems like the issue isn’t with the (simple) attenuation/resistance circuit.
So I contacted David from Antumbra and he suggested to add 2 100k resistors between ground and one of the switch pins. I tried this and it’s gotten rid of the high pitched noise 
I don’t have enough of a background in electrical engineering to know/understand why this fixed it. Anyone have any idea?
The bleed on channel 4 is still there, although it’s only noticeable with very high gain so not really a problem in practice.
I’ll build a second one and do a comparison next weekend.