The only reasons the brass doesn't chamber easily would be inadequate sizing or, less likely, the brass is too long for the chamber but I assume you checked for this. You can't size completely up to the head/belt with the usual dies. A solution to this problem would be the following die:
Inovative Technologies Die
I don't think the need for this die is common but it may fix your problem. I've had the die for several years and have never had to use if for the several belted magnums I reload for so I don't think everyone loading for belter magnums needs one.
Regarding the 340 WM brass you resized to 300 WM; if it chambers easily, I would shoot it without worries.