I think there are several issues mixed here. Hydrostatic drive, cylinder circuit, and possible splitter circuit.
Hydrostatic drive is 'closed circuit' where oil goes from pump to motor to pump without returning directly to tank. Return side is under 'charge pressure' of 100 to 400 psi for several reasons (mainly pressure into the pump without cavitation, and for dynamic braking). A separate charge pump maintains the pressure on the low side.
Speed and direction are controlled by stroking the pump swash plate. No valves for control of the motor.
Open loop circuits (motor or cylinder) go from pump, to flow control valve, to cylinder, then back to tank and atmospheric pressure. Inlet to pump is atmospheric pressure. (Some big industrial open loop circuits have charge pumps, but not what I am referring to here.)
A cylinder can be run off a hst pump, but it (usually) needs to be a double rod cylinder with equal areas on each side. Otherwise the oil going to the cylinder is less (or more, depending on stroke direction) than the return to the pump, by the area ratios, and the pump won't maintain its charge pressure.
If the drive is a hydrostatic, with belt to the engine usually, or maybe direct drive, there will usually be two separate hydro pump packages stacked together. One for left wheel, one for right wheel. Or, is this a single pump driving a motor into a differential axle?
Usually a hst pump has a built in charge pump. Sometimes the small hydros do, sometimes they have one separate pump built in somewhere for charge supplying both wheel drives. Often the small loads such as mower deck lift simply tap into charge pressure (with appropriate sequencing valves to prevent the cylinder from dropping the charge pressure too low) rather than a separate lift pump.
I am going to guess the lift is from charge, but either way probably 2 to 5 gpm max.
Running the splitter cylinder from the HST can be done, but the circuit design is way beyond a homeowner project.
I think the project could be nice, mainly to get self propel and run a conveyor motor.
However, I would look at driving a new 2 stage splitter pump off the engine somewhere. Belt drives put side loads on the pump bearings, most are not rated for that, and you need either an overhung load adaptor, or external bearings, which are hard to line up.
Belt drive also limited on hp, unless you try timing belt design.
Can you couple it the flywheel/fan end someway, instead of the drive pto out end?
That would avoid the OHL. Not sure how strong the fan end crank is.
Another option, find a through drive pump but I don’t know of any two stage ones.
Next option, pull out the wheel drive HST pumps, drive the splitter pump directly, then tap into the splitter pump to run the wheel drives open loop. Needs some circuit desing to prevent heat, but could be done.
Of course there are tank mods, return filtration, and possible cooler needed, but it is all ‘possible’.
I’d sure figure a way to use that engine and hp though. Could run a 22 or 28 gpm two stage pump on a tradtitional splitter. and have electric start.
