Just keep in mind that you would be adding an engine, pump, tank, filter, and possibly valve, plus a bunch of hoses and fittings. So essentially building most of a log splitter. You could probably buy a stand alone splitter for the same or less $$, and a lot less work.
As for your existing setup, I would first get a gauge on the hydraulics and see what pressure you are reaching vs the tractor specs. As earlier suggested, the pressure may be low relative to specs, and bringing it up to spec will improve performance. I would not increase it any more than 10-15% over spec, and I'd think twice about doing even that. Any tractor damage caused by the higher pressure may be difficult and expensive to fix on an older tractor with limited parts availability, etc.
Also as suggested earlier, the easiest "fix" is to increase the cylinder size. That would be a pretty easy and affordable swap. The down size is that the splitter will run slower, so you are trading time for splitting power.
If you are going to change to some other source of hydraulic power, whether driven by a separate engine or a PTO driven pump, I would carefully compare the costs vs buying a stand-alone splitter. I think you would be hard pressed to build a hydraulic system and pump for less than a purchased splitter. Hydraulic hoses alone will cost $50 to $200 each depending on size and pressure rating. And you would need to carefully figure out the flow, pressures and splitting force. including whether or not to use a 2 stage pump.