I ended up trying a bunch of ublox modules and their PPS output was almost always the same (LEA 5T, NEO 7N, NEO M8T iirc). Fairly stable, but with visible steps in the adjustment size of the PPS pulse. In the modules I tested, the Trimble Resolution SMT had the best stability so I used it in my similar attempt to discipline a PRS10. Works great, don't have a more stable reference to compare to really, but also the SMT has some glitch after about a month of uptime where the PPS pulse either stops or fails to be recognized - in the time I had it running it happened consistently, even though between the module and the PRS10 is just a level shifter.
In any case, I managed to pick up a Jackson Labs Fury since then, so when I can get my antenna situation worked out at the new place, maybe I can make some stability measurements again around a similar noise floor. It uses a Motorola M12+ GPS receiver, which they claim is a top performer despite being a bit of an older model by today's standards.