Your replies were just about what I expected. I have a turret press, currently set up for 5.56NATO and on that I do just what Dave H. suggests. Priming is done away from from the press with an RCBS priming tool like this one. I really like this tool, it's reliable and quick.
Decapping and priming could certainly be done separately and primed cases fed into the Lee 1000 to be sized with no decapping pin in the die. It means handling them 2 extra times, so I'm not sure if that would be faster. I may keep on fiddling with the priming system. Maybe I'll be the guy that comes up with a fix.