Another note on the ripple at 200 mV/10 V...
As mentioned, this only happens when a specific relay switches.
So the path must be carrying this ripple—or rather, this interference.
I was able to trace the path back a little, but at a certain point it goes “down,” and I can't get to it while the unit is running.
A schematic for this section would be a godsend; I was in touch with Owon, but I think once they realized I had a Voltcraft, they went completely silent.

(Which is a common issue with Chinese manufacturers—99% of the time, their support staff are people who don't know anything about the product because they work in sales.)
Be that as it may, I'm going to continue anyway...
Why? Because it appeals to me—I don't actually need the scope at all.
But the thrill of finding and fixing it...

Right now, I’m trying to figure out where the GND switching kicks in.
If you set the coupling to GND in the channel menu, everything goes flat.
So where exactly does it switch to GND? That would help narrow down the search area.
We’ll see...