It seems to be working now, and I'll tell you what I did to fix it.
First, I think the main problem is the water is too clean, with only a single small fish in a 40 breeder... and the skimmer was putting in way too much air. Think of it like an old engine with a carburetor -- you need to find the right fuel-air mixture (fuel is the proteins/organics in the water and air is... air). The general advice of starting with the air wide-open and closing it until peak bubble just doesn't work with so little "fuel" to work on.
The fix is to close off the air completely, then open it just a tiny bit and wait for a stable foam head to start to form. Foam is frothy, not rolling bubbles... you need stable/static foam on top. Then start opening it a little bit at a time, leaving it for an hour or so after each change. When the foam head starts breaking up and it turns into a "rolling boil" on top, that's too much air... turn it back until the foam head forms again. That's where you want the air.
Then start to close off the wedge (again, a little at a time, because it takes some time to stabilize) until the foam is just about at the top. As the foam accumulates, some will overflow into the cup. And note the water level will be very high when doing it this way... well up into the throat of the skimmer. But it will be stable.
I've had it running for about a week and a half this way and I'm getting nice medium-brown liquid in the cup with some sludge on the rim and edges. Once I've got more bioload, I'll return to tuning for that higher load, but I think for now, this is what's best.
Also worth noting, I did not need to raise it for this to work... it's still in 7" of water. And I have the pump running at 100%... so lots of water being processed.
I hope this tuning method helps others who are struggling with the general tuning advice, which seems more geared to established tanks.