The tightening collets on both Lee an Hornady dies have only two cuts, no wonder they can slip. A couple of simple Dremel cuts should help.You should see the collet on my Elu/Dewalt router ! The dies are short, barely fitting their Classic Cast press. I like their new screw clamping lock rings.
In the "Ask Gunwriters forum" there is a thread on 338-06 necking up problems with a Redding die. I posted on that thread my numbers with a Lee die. You judge.
Lee service isn't as good as it once was. When I screw up, I don't mind paying for the parts .I stripped a collet dealing with some 338-06 Weatherby brass. I don't know what happened, I've already made lots of 338-06 out of Federal 30-06 with zero problems. They were a little tight lipped about the size of the collet thread, as I had to chase the remains of the collet out of the die. Enough pestering, I got an answer. They were much more forthcoming 30 years ago when started and had problem with the pot metal linkages on their press.
