More thoughts:
-Cylinder: 250 is most likely psi. Search on the model number and see what Parker has. It is likely a very old model and probably not on inet. Parker is HUGE in hundreds of markets, not just fluid power.
-Was this a very old machine, running for the previous owner years and years, or something just built recently of old parts? i.e. is it a design issue, or a breakdown issue?
-Did the PO run the engine at partial speed and have satisfactory service?
-The reason all this clicks is that the Vickers PV series piston pumps were rated for 1800 rpm max in the industrial version. In the 80's they came out with an M prefix (say MPVxx) for mobile equipment. Still it was only rated up to about 2200 or 2500 rpm, depending on pump size. (Smaller = faster allowable). M was also heavier cast housing for pressure spiking, but that is not likely relevant here. If you are running the engine at higher than the maximum pump speed, it will cavitate, aerate, and possibly lift the block and suddenly drop to very small flow, and eventually mechanically destroy itself.
RPM limits were determined by two design issues:
1. The fairly restrictive inlet porting in a piston pump compared to gear pump. Flow has to turn 90 degrees, has to be quite small because of area available on the valve plate, and the inlet flow starts and stops with each piston passing the valve plate. All of this means the restriction is high, so speed has to be kept down. As inlet absolute pressure drops, the issue that I brought up earlier with case pressure vs. inlet pressure becomes serious. Hydrostatic pumps have the inlet charged at 300-400 psi to overcome both of these issues.
2. An open loop piston pump has unbalanced forces in the rotating group. That is solved by a big spring in the center of the block. However, as rpm increases, the forces tend to skew the rotating group so the rotating block is not forced perfectly flat against the stationary valve plate. With a very tiny gap, there is leakage, and there is pressure applied to the valve plate in bad places which separates the two surfaces even more, and they lose the seal. It is called 'block lift'. Hydrostatic pumps solve this with the charge pressure system but can still overspeed. Usually, with overspeed and blocklift, there will be a sudden 'bang' noise and the pump output goes down to almost zero. There is massive flow into the case briefly (sometimes milliseconds), case drain gets overwhelmed, the shaft seals can blow or the case can crack. It usually will not reset itself until the pump goes to a very low speed, or maybe shut completely off and restarted. A hydrostatic pump can suddenly lose all engine braking and basically 'freewheel' the machine if it is overrunning down a grade.
Even if they don't lift the block, they can wear oddly on the piston slippers and swash plate and lose sealing efficiency, especially if running with an open center valve and under very light load conditions, (no system pressure holding the pistons and slipper tight together) and no lubrication to the slippers. They really don't like light load conditions, which this might have been if the control valve is open centered.
Does any of this describe what you were seeing?
Open loop gear pumps have a LOT of advantages in simple applications.
-I doubt the pump is feasible to rebuild. Parts will be really old, or probably aftermarket. Eaton/Vickers is way out of the market for those pumps in the industrial world. Newer pump designs are smaller, higher pressures and speeds, faster responses, and way more control options.
The valve plate is not a loose part. The entire cast end of the pump is replaced. Rotating group and front bearing is replaced completely. The swash plate is who knows condition. That only leaves the housing and the shaft.
However, it might be worth sinking more money into it just because of the shaft and mounting issues you'd have to deal with to replace it.
-Mount is likely an SAE A or B, no problem there.
-With the clutch or in & out box, the shaft is probably splined and oil lubricated. Standard SAE splines, likely no problem. However, logsplitter two stage pumps will almost all be keyed straight shafts designed to run directly from an engine via a jaw coupling with no oil bath.
-If you make an adaptor housing of some sort and have a jaw coupling to be able to use keyed shaft pump, you will have to seal the original mounting pad on the pump drive against oil leaking out, and need a stub shaft from spllne to the jaw coupling, and have to control axial movement of that stub shaft, and probably other issues I am missing.
-You could gut the piston pump, put a rear housing on it that has a through drive pad with keyed coupler, and put a log splitter pump on the back. Vickers had rear pad options but somewhat rare in these smaller sized pumps, and I doubt many spare parts are still around in the system without paying hundreds of dollars.
-You could use a two section pump with external unloading and check valves, but I don't think you want to go there.
-Or, you could use a single section, spline shaft pump. Surplus Center will have some selection of these. If you are used to the speed of the old pump single section pump should be fine. That is essentially what you have now. The pump will be at max displacement until it compensates back on pressure. It is not a varying output flow in this application.
-Another alternate, buy a harbor freight engine and pump and sell the other parts. This is probably cheaper than adapting a keyed pump to the existing drive, but more expensive than a single section splined pump to the existing pump drive.
-Either way, you need to verify an open center spool valve, and verify there is a relief valve in the system.
-Overall it is a 'wool sweater project'. Don't pull the loose string hanging out of a hole in a wool sweater. We've all been there with cars, motorcycles, etc. etc. By the time you replace pump, engine, valve, and cylinder, there is not much original left.
-I would get a single section gear with spline drive, put it back in the clutch box, change the suction plumbing, add a return spin on filter, make sure you have an open center spool valve with a relief valve in it, and run it at a very low pressure. With a 6 inch bore you don't need much pressure. The air cylinder may survive, but I am not recommending or condoning it. Get your work done, sell it, and buy a more modern unit with faster two stage pump.