I would guess the crayfish eat the snails every opportunity they get.
Theoretically mystery snails can co-exist with ramshorns. But just note, I had a ton of ramshorns, but as my mystery snails grew and grew, dropped eggs, and those grew and grew, there are no ramshorns to be seen. I still see some MTS, but not that many. Those mystery snails, without preditors and being so much bigger, will eventually take over I would guess, they certainly did in my tank!
I keep the water level a couple inches below the top. Apart from anything else, it discourages my female snail from forcing her way out to lay on the side of the HOB. I’ve only let one clutch develop so far, and it was laid right below the rim and did just fine.