OK, I'm a goose 
Obviously my build really hates power supplies like the 1-Spot. Although the EM was running off a battery, my LM386 test amp was using the 1-Spot for its power supply. Today I switched back to my normal amp with the EM running off a battery and it's nearly silent except for the most extreme settings.
At least I've got a workaround now. I'll see if one of my mates has a transformer based power supply and whether that's any quieter. I might have to finally invest in a proper isolated power supply.
Hi John!
I'm glad you have found cause of the issue - I know how this kind of issues can get frustrating!
Extreme settings are noisier principially, so you are probably OK now.

About your PSU: is it
this one

? Well, normally I would simply say
get rid of it (I'd never choose switching PSU for pedals), but Visual Sound =
R.G. and R.G. usually knows what he's doing - maybe you could try to consult with him? There still may be some simple solution how to make your pedal and your PSU good friends

Good luck, T.
Btw. thanks for the clock readings! - was it maximum where you could get without dropouts?