It is more likely that your issue is with your Sizing die than your Seat/Crimp die. This is because your bullet should be held in place by neck tension, not the amount of crimp you're using.
Your Sizing die has to be all the way down until it touches the Shell plate. I would also recommend, when setting up your press, you use brass with all identical headstamps...I personally don't load R-P 9mm cases at all; too thin.
It is also possible that you are over crimping your loaded rounds. When you overcrimp, you are compressing the bullet and the case mouth. The brass of the case springs back; the bullet, not so much. This often allows the bullets to spin in the case.
It is also likely that your "older Hornady 3 set dies" are roll crimping your cases. Older Hornady 9mm die sets had a Seat/Crimp die that roll crimped rather than taper crimped. This would provide an excellent opportunity to get a separate Taper Crimp die and separate your seating and crimping. I've never crimped with my Seating die, except when starting out with my original RCBS 9mm set
As already mentioned, you need to set your seating depth with all the die stations filled with cases