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I'd spend the $$ on some Redding competition dies which would include a neck sizer and a FL die. I'd stick with the Lee if its working for you. I use a Redding Ultramag press but I don't see that particular SS press as a necessity. I'm no expert but subscribe to the notion its the dies that matter most.
Incidentally, I wouldn't worry about breaking the bank reloading .338 LM. You'll save enough reloading these suckers to justify just about any purchase you want !!