I have no idea as to the marital status of your parents but I am always willing to talk to you. :sidelaugh:
I often leave threads like this alone in the hopes that other members will post their thoughts, suggestions and experiences.
As I see it, what you want to do is desirable but complicated by the lack of available room. The sleeve hitch is connected to the bell crank by way of a 1/2" thick piece of flat bar that is bent in several directions . There is precious little room between the inside of the rear tire and the frame/fenders of the tractor, regardless of model. And when you get forward of the tire, you then have the footrest and parking brake in the way.
The actuator arm on the hitch points upward but at an angle. My thoughts are that you must make a new arm that bolts to the stock one and points downward, below the hitch. One hole would have to be drilled in the hitch frame to accept a second bolt for this new arm. The cylinder would mount below the frame in the most convenient spot and perhaps a link would have to be fashioned to connect the new arm to the rod end of the cylinder. The length of the new arm would have to be worked out in accordance with the amount of stroke of the cylinder but I think that an OEM middle lift cylinder could be adapted for this task. That cylinder is designed to work on the existing hydraulic system. Pressure and flow issues would be non-existent. No problems with adding a selector valve either for separate control.
I am speaking off the top of my head so that you have something to think about. Obviously, it would be helpful if you had a spare lift cylinder around so that you could try positioning it under the tractor first to see if any of this is do-able. I would be reluctant to choose a smaller diameter cylinder for fear that it would not lift all of the loads you might place on the hitch. After all, the lift relief is usually set at 575 PSI to protect the cylinder and everything it is mounted to.