...So, any idea what I have?
Offhand, no. The casting roughness on your piston, around the recessed sides, convinces me that it is indeed an aftermarket piston offering. I seem to recall some early Wisecos looking like that. They still have ringsets for their 80mm pistons, but not for the 256 80mm pistons.
It's just that we're in the same boat with these non-existant '70s rings.
Yours being a 477-type piston affords you more options. Could just get new 447 80mm pistons and rings, and you'll be up-to-speed with the newer ring geometries.
MikesXS has rings for the 80mm pistons, but the top ring will be 1.2mm, and the widths for the 2nd and oil are unknown.
Those Toyota rings look promising, but they're 81mm. A bit much.
We need more ring geometries. Like for the TX750, Alfa 1750. I have a set of 80mm (Moto-Guzzi, I think) rings buried somewhere. Need to get their geometries as well. There may be others. I also need to catch-up on ring backspacing criteria.
I'm fully expecting that some type of mix/match will have to be cooked up.
Your description of your oil ring setting depth is odd, makes me wonder if some previous ring/piston match game has occurred.