Gotoh installed, tuning stability still lousy.
I think the problem might still be at the nut. I lowered the string tree bar to give all strings more length to hug the nut, ensuring the locked nut would not allow string slippage. Tightened the nut screws pretty well.
An observation I made is that, with the locked nut, mind you, if I lower the bar and strike the strings behind the locked nut that the string tension goes down, especially on the G string. (Not seeing this with my wonderfully working FR on my MIK LTD SN1000FR).
I wonder whether the nut itself is not screwed down tight enough. It is just the two small wood screws from the top, and when I replaced the Special nut I already had to be really careful as I think they were overtightened before, and they might not give enough grip now. I cannot see or feel the nut itself move though.
I think the neck itself is not a problem. I can pull the headstock back and forth pretty hard (what some Les Paul players would do) and the string tuning barely moves.
Here the Gotoh:
View attachment 101564