Try to rework your off the wall press so that it is solidly into the studs You should be able to to anchor it sturdily enough not to pull off.
If you're going to stack 6 molds 6" high, I'd shoot for at least a foot of stroke in the cylinder if not 18. Piston diameter depends on how much air pressure you have available and how much pressure you are looking to achieve at the cheese. If you have 150 psi air and a 2" diameter piston you'll end up with a bit over 9 psi at the cheese. The force generated is proportional to the square of the area, so 150 psi air with a 3" piston will get you over 20 psi on the cheese and 37 psi with a 4" piston.
As for plans, your Dad seems to have hit it pretty well with the current design. You'll need some way to keep the molds aligned under pressure. and a frame that will take the forces generated by pressing. With an 8" mold, you'll need 50 pounds of pressure to generate each psi on the cheese. Someone on the board made a pneumatic press, search for it an it should give you an idea. You'll just need to make it taller to hold 6 molds and allow for the stroke.