Primer advance assist: Custom made tool.
I second the notion of looking for burrs. Also, a bit of silicone spray dry lube might help. But I would not put it on top of the graphite. I would wash again, first.
Using a hand priming tool with a progressive press just seem wrong. It violates the concept of "progressive" adding extra insertion/removal cycles and paying extra to add steps that should not be necessary in the first place.
I did not like my Pro-1000 presses for several reasons. One was the primer feeding. If you try to go too fast, the primers don't have enough time to get positioned on the ram. I used to pause just at the instant I saw the column of primers in the ramp advance. Sometimes, if it looked like they did not advance as far as usual, I would take a custom-made tool to make sure the primers were fully advanced. (Favorite material for custom tools: unbent paper clip) That cured almost all my primer feed problems completely. But it did slow down my production rate.
About my production rate: I was never comfortable with operating my progressives. Watching multiple simultaneous operations made me nervous and cause me to slow down as I chanted a mantra that ensured I left no step out
stroke
spent primer drop
powder drop
stroke
case feed
primer feed
primer seat
bullet place
etc.
I finally got wise to my own limitations and style and got a Lee Classic Turret. I could not be happier. My production rate is about the same as the progressives, caliber swaps infinitely faster and the new primers are 'way above the primer dust and VISIBLE when placed in the primer arm's cup. Best of all, I am relaxed when I reload now.
Not suggesting it for you. Your style will be different than mine. Just food for thought.
Try the dry silicone spray lube. Then the primer advance assist tool if necessary.
Good Luck
Lost Sheep