The thicker Gator checks will also do as you described in picture. The cure is to first crimp on (do not size) the thicker check using the Lyman or RCBS base first sizer. Next full length size nose first in the Lee.
Hornadays do work better in the Lee sizers, but the metel thickness is thinner and weaker. Resulting in checks flying off harder alloys when fired. Hornadays work best or stay on best when using softer alloys at lower velocities under 1700fps.
Thicker 22 caliber Gator checks seem to grip all alloys better....less flyers if bullet fit is correct.
Here is a good 22 cal bullet.