I'm not sure I'm using the Lee Case Trimmer correctly (on my .44 Mag, -'06 and .375 H&H cases).
when I put the proper shell holder in the chuck, if I screw it all the way in, then the case head doesn't have room to slide in. Yet if I back it out so that the case head can just slide into the shellholder there is "slop" between the chuck and shellholder. This can't be right and it drives me nuts for lack of precision!
What am I doing wrong?

Scott - you back out the chuck, slide in the case, then tighten it up again. It holds the case tight against the face of the check, which is also the datum point that the cutter pilot indexes against.

I use a zip trim, I use the universal 3 jaw chuck, Its a little quirky to use beause the jaws sometimes don't want to engage, I found for me it works best to hold the stem of the chuck with 2 fingers and turn it to engage the jaws, if you are using the shell holders that came with your length gauges, those suck I couldn't get them to work