For full length sizing I use the oiled stamp pad method and inevitably lube gets on the shoulder. I don't stress by getting an itty bitty cloth and wiping if off. The cases are only finely filmed, which is all that is needed after all. I have never dented shoulders and never had a case jam in a die. I sometimes use Imperial sizing grease (tiny tiny amount) and wipe that on using fingers then straight into the die, no probs.
As always, too much of anything is bad fer ya.
Excess lube build up inside the die as @ChrisW points out is one that can sneak up on you, but the in the OP's case it sounds like excess lube right from the start.
Brakleen is good stuff. I buy it a box at a time. Also used during my barrels cleaning. And lots of other uses but never yet used it on brakes.
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