I have managed to get the (almost) stable tones. In some special cases I am still getting 2 options, but looks like proper reset sequence (when cycles are not counted) does the job. My current sequence is:
SKCTL = 0
AUDF0 = 1
AUDF1 = 1
STIMER = 1
AUDF0 = xx
AUDF1 = yy
SKCTL = 3
I have also noticed that setting the register (CS0=L, CS1=H during 1 clock cycle, both edges) does not take an effect when the value was not changed.
For example when using unstable tones - tone changes after first write and another write does not change it. Writing something different then the previous value takes an effect and the tone is "random" (if unstable).
However, the older chip revision which comes from 5200 board (CO12294-03) acts differently. Every write takes an effect and the Synthpopalooza's table for distortion 12b ("smooth", divisible by 3) is not stable (at least in my case; same setup, only the chip was replaced). It was stable on CO12249B-01 (from 65XE).
Do you know what are the differences between chip revisions?