It sounds like your cases aren't fully formed yet. It may take 2 or 3 or more firings to fully fill out the shoulders & the headspace depending on the brass & your loads. Did the unsized fired cases chamber hard? Dont bump shoulders until the brass gets hard to chamber. Then slowly turn the die in until the bolt closes easy.
Did you remove the spent primers before measuring? On firing the primers back out a bit & can add a few thou.
This is a personal thing but I wouldn't use a Lee die unless there was absolutely nothing else available. Maybe they've improved in the last 30 years. Try the above first. Everything may resolve itself & your dies may work splendidly.
