An inexpensive chamfering tool might help.
When you insert (start) the bullet base into the case mouth, carefully ensuring the case mouth is not catching anywhere on the bullet base will help tremendously.
If you have not used the case mouth bellng mandrel well enough, you can do it more thoroughly (check the bullet base to case mouth fit to tell you when this is appropriate).
If the mandrel is worn, you can get another from Lee.
If your bullets are oversized (get a set of calipers) you might consider an oversized mandrel. But oversized bullets can lead to pressure problems.
P.S. Your comment about full-length resizing confuses me. The Lee Loader does not full-length resize. The mallet powered tool set is not intended for full-length work.