I find it amazing, that we come up with so many different ways to do the exact same thing. I really Like your BIG RED MOUNT. It looks to have been repurposed from a bracket of some nature.
There are some companies that make mounts and handles for loading presses besides the press manufacturers. As with most web pages, the photos never give the critical information you need. Like height, width, and depth, along with back-set and different angles of approach.
In looking at your latest photo of the Lee turret press handle, The way you grip the handle; looks to put several different stresses on your right shoulder. Weather you clasp over the top or vertically grip the rubber changes several muscle and tendon attachment points at your shoulder.
May I suggest you start with the handle/grip problems then start on the height issues.
In my last house I had a dream LOADING ROOM, 12' by 15', with a 7' bench along one wall and turn around , there was 9' of "L" shaped bench in the corner. (This took 15 years to perfect, and didn't start until my daughter went off to college and I took over her room complete with pastel walls with pretty flowers stenciled on them) At one point I had 2 Rock Chucker Supreme presses mounted at different heights, 2 progressives (a L-N-L AP & a 450/550)) and a Redding T-7, PLUS changeable plates with more loading presses and bullet sizing presses that I could switch as needed. NOT SO MUCH ANYMORE! I have a 5' bench between filing cabinet and gun safe and a few shelves in the laundry room. The 550, the T-7, and my plate system (usually not mounted so I have some space to do small projects). To load shotgun shells, those pressed have always been mounted to 3/4 plywood and clamped to the bench. Only now there isn't room, so I "C"-clamp them to a workmate in the family room. (Shot spills in Mama's carpet earn me much grief, that I deserve!)
I started loading 37 years ago,. My bench(s) have changed, my space has changed, even my location has changed twice. But I keep loading and improving the process! Good luck figuring out what you need and balancing it with what you are allowed to get!
Ivan