"I have heard of folks using so much force that the aluminum top cap pops off..."
Lee makes that cap of aluminum so it can act as a "fuse". It's the cheap "weak link" and will blow out if we put too much pressure on the die, it keeps us from breaking the press or the die!
Seems the bullets are slightly undersize, nothing the die can do about that.
The open diameter of the collet neck only need be large enough to allow the case neck to enter, it's not a critical dimension at all. Ditto the dimensions of the collet and closer taper.
"Grinding" the neck diameter of the mandrel will fix the problem easily. Chuck the lower part of the mandrel, the primer pusher end, in a high speed drill motor. Use a section of some black sandpaper, silicon carbide actually, held against the mandrel to do that. Using a grit of anything from 150 to 220 should do nicely. There is no real benefit in "polishing" the finished mandrel with a finer grit but it does make it look nicer.
Decrease the working (actual neck contact) portion of the mandrel's diameter no more than 1.5 thousant, that should be all you will ever need.
Lee would likely do it for you but you can do it yourself much faster!