While the 'result' is a harder leather, the primary goal is to 'compress' rather than harden. The secondary goal is to cause the silicates within the cell structure to migrate to the surface. Remember, it's those silicates that are needed to do the abrasive polishing with a bare strop. If you just wanted 'hard' leather, you could use a piece of rawhide. Or not use leather at all. Cardboard works well when used bare, as does the cover of National Geographic. Not as good as bare leather (as the abrasives in them are of a larger grit size,) but both are hard, cheap, and easily found.
With that secondary goal in mind, 'my' thinking is that it would be better to roll longer rather than press harder. If you look at the Horween video, you can see their process. It's a repeated rolling action rather than a single hard pressing. I'm sure there are machines that could 'press' the leather down with a single stroke, compressing it as thin as could be in a single time-saving action, but that doesn't seem to give the desired result... Cordovan Leather, the closest approximation to the Russian Red Leather process. That old process involved pulling the hides back and forth over the rounded ends of logs for several days, rather than just pressing them down with heavy weights.
When I make my strops, I make sure that the leather has been thoroughly wetted, allowed to dry for an hour or so, then with the leather on a smooth hard surface (the marble kitchen counter,) I use an ordinary rolling pin and the same pressure I use for rolling out a pie crust, rolling end to end, and occasionally turning the leather over. I put some good music on, and roll until I'm so damn bored I can't roll any more... usually about 30 minutes. This produces an excellent piece of leather to use for a bare strop. Then it's up to you how you want to complete it; bench mount or hanging.
Stitchawl