IDK about the Hornady PTX, but the Lee dies and dispensers work. The biggest issue is that the 650 toolhead is pretty tall/thick, so lots of dies (including most Lee dies) don't have enough threaded height/length to reach far enough down for operation and still have spare threading for a Hornady or Lee lock ring. Dillon makes some very thin plain lock rings that are just plain nuts (as in, hardware store nuts) with no setting-retention mechanism (no set screw, no rubber ring for friction) and those take little enough space to allow Lee dies to work.
But once you get the dies to the right dept, they interact with the case the same way as in any press.
But once you get the dies to the right dept, they interact with the case the same way as in any press.