I am at a total loss as to why after tumbling the cases will not fit the shell holder. Would there be a possibility that there is a piece of brass lodged in the groove of the shell holder, if they worked before tumbling then they should work after unless you are really beating those cases to death with some type of heavy median?
I looked at a couple of reloading books that I had close by and one says that the case should measure .375 and the other says .376. There is such a thing as a Small Base die I don't think Lee makes one but RCBS and Redding do but the shell still has to fit the shell holder before you can use the small base die. By chance will these shells chamber in your rifle? What kind of rifle are you planning to use this brass in?
RHB