I looked at making a shooting bench off one of these. They are heavy duty devices and have more than enough weight and stability to load off of.
What I would do is mount the Press to a piece of plywood big enough for all your stuff and have a chunk of 4 x 4 bolted to the bottom to clamp in the Jaw Horse. I was going to do something similar with the Shooting Bench idea where you had a table top with a 4 x 4 bolted to the bottom to clamp in the Jaw Horse.
I have made several things like this over the years, and my first Reloading Bench was a 2' x 3' piece of plywood with a 4" wide strip screwed to the bottom held in a B&D Workmate. I still have it and could have it back up and running in an hour.
I needed a tooling plate/platform to hold in the vise on my mill to machine the dashboard for my Jeep. I got a piece of 3/4" plywood 4' long x 1' wide and bolted a nice 4 x 4 to the bottom. This unit gets clamped in the Mill Vise on the mill. I then drilled two holes for dowel pins to provide a backstop that is parallel to the X axis on the mill. It is close enough for plate work on the mill and since it is plywood you can mill into it and not hurt anything. I just used it again last week for drilling some holes in some panels I was working on for the Navy.
The same concept would work just fine being clamped in the Jaw Horse.
The reason I din't do it is because the Jaw Horse weighs about 35 lbs and was too heavy to be throwing in and out the back of my truck several times during a day of shooting. They are more than up to the task stability wise.
Randy