Not so easy to say, but if the 20 min test was all out at 256 W then a CP of 251 W sounds significantly too large to begin with. Still, your reasoning on interaction of APR and CP is qualitatively right. I have similar issues, but do have sufficient history and also alternative data to “know” my CP better… and set it manually.
If you do not know your CP well, I would suggest to do the full atheltica test week: MAF, power profile, and the 20 min test on subsequent days. That should yield a complete profile that the atheltica algorithms should robustly analyze…