Possible? Yes. Worthwhile? That's the big question.
The highlighted part of your post is where the problem lies. A GT sized FEL uses 3-5 gpm of hydraulic flow. A top end hydro flows up to 14 gpm, and the hydrive in a Case GT flows about 9 gpm. While it is possible to run two hydraulic systems off of one pump by using a flow divider, control becomes somewhat problematic since a specific flow rate will be dedicated to one or the other system across the engine's rpm range. In particular, a FEL that operates at only one speed is not fun when precision is required.
The Case tractors have a specialized drive control valve that allows both functions. Since I have never operated a Case with the hydrive system, I can't really comment on how precise the control is for either function. I can comment on the controllability of a hydro in conjunction with a dedicated auxiliary FEL pump, and it is very good. I wouldn't want anything less.
Surplus Center sells a hydro pump and several hydraulic motors that would work for your drive modifications. Coupled to the second transmission, they would give you three ranges, which is a very good thing. They also sell utility pumps that would take care of the FEL duty.
Note that a pump is sized for the task at hand. Too big and FEL control is out the window, too small and the FEL will be too slow for many tasks.
Cooling for a correctly sized FEL system is not a problem, and a hydro/gear motor drive system will be relatively easy to keep excess heat under control.
