Some very old Weaver rimfire scopes had you remove screws from turret - front ring slid off, then remove turrets, then slide the rear ring forward - then re-install the turret boss. I do not think they had a front bell though. Is it possible that those rings might have two parts to each - a clamp part that mounts to the rifle, then the "top" part of the ring slides forward off that? Some weaver type rings have only one tightening screw to hold the scope - the other end of that ring is in like a notch or a clip that would hold it, but could not tighten it. FYI - As shown in your picture, that scope is upside down in those rings - horizontal (windage) adjustment knob should be to right side - elevation knob should be on top. Assume that the rings did not grow there - someone put them on - maybe you can figure out how to undo that.
There are also some rings that the "clamp" screw that fastens that ring to the rifle is also holding the ring left and right half together - it might need both screws removed completely to separate those rings from that scope. You are correct - "prying" those clamps to get them off seems to be a barbaric way of doing it - certainly not likely re-usable after trying that.