I was rereading this thread and saw this reply so I went to my shop, got my 30-06 Lee Loader out and primed 4 cases (HXP). I used CCI LR primers and all primers were about .003"-005" below the case head. I didn't try any of my other Lee Loaders, as I remember checking all primed cases with my finger looking for high primers. IIRC all primers seated on my Lee Loaders were below flush...
FWIW priming is easy with an arbor press and I can't remember popping any primers when I used a dead blow hammer...