My Geishas are fully tuned with consistent one degree bases and two degree side bevels, and they're now going through a few hot scrapes! It turns out that my Ski Man base beveler has a distinct wobble with or without a file inserted, and the wobble changes a file or stone's angle enough to feel like the edge needs re-filing. I picked the side of the wobble that puts the edge in contact with the whole width of the file/stone, and while carefully keeping the wobble steady I straightened out the Geishas' base bevel and added a more mirror-like shine all around with the Arkansas stone. Now all my edges are all shiny and sharp, and it feels like all is well with the world.
I bought the Ski Man beveler because I used it at REI's waxing and tuning workshop, so I brought mine down to compare it against one of theirs, which was indeed wobble-free. The trouble seems to be the bevel adjustment piece, which unlike the aluminum body of the tool is cheap white metal that is probably bent or warped. I really knew better than to buy an adjustable tool, even one made by Wintersteiger, but my experience in the REI workshop caused a momentary lapse in judgment. Fortunately the site I bought it from will take it back, and I'll get a fixed angle beveler with the proceeds. I've learned my lesson!!
ETA: BTW, the problem wasn't that the angle adjustment piece wasn't holding the angle; the piece's two feet, which rest against the base, aren't square with the body of the tool, like a table with one short leg. Bad QA!