I built a few back when I sold skinning machines. Most people want the animal around 32-36" off the floor for standing to skin, adjust for your own body height.
Personally if room height is the concern I'd choose a roller style skinning machine.
A&J Skinning Machines sells a nice one I designed many years ago. They have since taken over building my designs with my permission and initial guidance.
With this style if you run out of pulling height, you just lower the critter and roll up more hide then continue the pull. If I had to start over with a new skinner this is the style I'd choose.