I've now got back my SK60XL from Schneider-Kreuznach, without action. They had noted some skew in the lens board, so I changed that.
I've done lots of various testing today with both my lens and the loaner lens, and cross-combining the front and back etc. Somehow it works better now. Actually I couldn't figure out exactly why, which is frustrating. I can speculate that the lens board did help my lens.
There is still some left-right variation, but I think it's reasonable now, I'm pleased with the performance. Also note that the Linhof Techno is a great flexible camera to use in the field, but it's not ideal for lens testing. A pancake camera with HPF ring would be so much easier to do lens testing with.
I'm now pleased with the performance. As you can see in the attached shot there's some variations between the copies (note however that I have refocused between copies), but now the worst case is about the same as the best case in my previous testing.
The crops shown here is of actual shifting (not the lens rotation trick), which means any precision errors in the camera is included too. However I did make lots of lens rotations too and there's some variation there too, ie the real shifting didn't make it much worse.