I am not sure I can quote exactly the book on the forum, but in the chapter “training for non-competitive lifters”, Jim does say that we should keep pushing rep PR’s.
In the 3’s and 1’s week, we work up to a single at no more than 95% of estimated max.
It is explicitly written to not hold off on the last set to work up, the last set always has priority.
You are right for FSL though, Beyond was written after 531 for powerlifting. I looked around the forum and found this
Where Jim is talkng about the 351 set up for rep PR’s, so apparently it would be OK to have 3x5… But Jim is talking about rep PRs, and there is no mention of singles so it might be better to just leave it out.
So I would do this twice, deloading every 2 cycles:
Leader (2cycles): 5’s pro + 5x5 FSL
Anchor(1 cycle); 3/5/1 + single on 3’s week and 1’s week