It stuck before you fired it? That means something didn't fit as it was loaded. So a couple questions.
When you say collet die, do you mean the sort of neck sizer die they sell? If that's it, and you used correct 6MM bullets in regular 243 brass, then you probably have it set wrong. Maybe you are actually squishing the shoulder if it goes in too deep. Did you reload a batch of them? If so, do the others fit the chamber?