When I'm loading BPCR cartridges, I'll first dump the powder into the case through a long drop tube. Then, the overpowder wad is pressed into the mouth of the case, and seated by the compression die. Next, the grease cookie (for paper patched bullets) is placed, followed by a lube sealer wad (same as the overpowder wad, just that it's next to the grease cookie).
To prevent it from sticking to the bullet, I'll have an alcohol cloth. The bullet base is wiped across it, then onto a dry cloth, then it's seated into the case.
Hiding in plain sight...