Clark it looks like you have got you a mobile reloading rig !
I would probably make it more complicated than needed , was thinking of a fabricated bracket mounted in the bottom of one of the seat boxes that would accept square stock (think receiver hitch) vertically cut to height with a plate on top to take the press the post pinned to the mount like a receiver hitch , pull the pin and lay post and press in the seat box . It could be made where it could be moved outside to the vehicle hitch if wanted.
Give me a little time I can come up with a complicated solution to a simple problem
simpler the better if it gets the job done.