Hi,
Without actually seeing the brass and die, I don't have much to suggest except to ask if you've deburred the case mouths on the outside, taken the die apart and given it a good cleaning, and are putting enough flare on the case to allow the bullet to self center on seating.
I've seen a little residue (shavings) from sharp edged brass when using the standard seating/crimp die to do both jobs in a single operation, though rings have usually been lead, rather than brass. Haven't seen it happen when seating and crimping in separate operations, whether using the standard seating/crimp die or the Factory Crimp Die.
Then, if you clean the die body exactly the same way you do your pistol barrel, with a rod, bronze brush, and patches, you may find a sharp or rough spot. If so, sometimes it's possible to polish it out, or the die may need to be sent back.
Lee also has some videos on their website that show some adjustments being done ever so slightly differently than the printed instructions describe. In one of those "a picture's worth a thousand words" fashions, there might be a helpful hint in there to cure the problem just thru a simple die adjustment. I've seen some problems with inadequate flaring, though most of them were with 9mm. The bullet can get jammed into the case off center (notice large bulges) and a portion of the mouth of the case can end up being sheared off ever so slightly. In my own limited experience, that's been more of a problem with lead bullets than jacketed, since they're usually 0.001" or more "oversized" from the jacketed spec.
Someone else probably has some better ideas. If you hear "Lee is junk, buy RCBS!" from a certain poster, that's NOT one of them. Nobody really makes "bad" dies these days, but a problem can happen with any brand...
Rick C