I had a problem with my FTP moving POI during shooting i.e. as the cylinder emptied. Fill and it was back on target, so obviously the front clamp was moving something. As I shot a course I was noticing that shots were progressively going to one side and I would add a few clicks to compensate until I'd added a full windage turn.
A few weeks ago I bit the bullet and took off the clamp, the shrouds and the bottom rail the clamp fits to so making the barrel and cylinder completely free-floating. The first thing I noticed was a surface mark on the cylinder and barrel which followed the exact shape of the 8 clamp along it's front edge. This suggests that the clamp was bearing onto the cylinder/barrel with enough force to mark the blueing. Not good.
I re-zeroed the rifle while it was about half full, then filled up to full and found no shift at all, nothing. I have shot the rifle now for a couple of weeks and everything is perfect, no shift, no need to rezero after every fill or watch the POI move as the cylinder empties.
If your FTP is shooting ok, then great, enjoy a great rifle and be grateful. If however, you are finding that it won't keep zero I would strongly suggest you try taking the 8 clamp off and seeing if there is any evidence of the clamp affecting the cylinder/barrel.