Unless there is some issue with cooling the engine at low rpm, (which aint likely) what other reason would you need to run at full throttle. Engines create less heat at lower rpms than at full throttle so I dont see the point. As for the hydraulics, the pump is rated at a max flow for a given rpm, and some pumps need to run a minimum specific speed in order to pump properly, But as long as you are turning enough rpms to meet the minimum requirement, the amount of flow is all you are really affecting. Pump rated at 10gpm at 3000rpms will still pump 5gpm at 1500rpms. Pressure is a little different matter, it takes 1.5hp to pump 1gpm , at 1500psi. Running the engine at low rpms will effect the amount of hp being generated. Low rpms could cause stalling simply because it isnt making enough power to pull the pump. This doesnt mean the pump wont build pressure and flow at lower rpms, just that flow will be reduced, pressure should remain contant, it will just take longer for it to build, and if the pressure builds to or above the hp being supplied, then you can expect stalling and bogging of the engine.
The Op's splitter is sticking and stalling the engine on the return stoke, I suspect the detent relief isnot properly set. There should be a relief at the handle to adjust the return detent. Back off the relief a little bit and see if this doesnt help with the sticking and stalling. You just want enought pressure on the return to get the cyl fully retracted and as soon as the hydraulic starts to build pressure, it will kick the detent and stop the cylinder. Yours is building to much pressure before the detent kicks out and this is whats stalling the engine. It is also possible that the relief for the push stoke is not set properly as well if the machine ram wont push the wedge thru the wood. If engine is only stalling on the return stroke and not the splitting stoke, I'll just about bet that adjusting the reliefs will fix his problems. Try adjusting the other relief for the push stroke in a little bit and see if this fixes the splitting power. If you have a pressure gage you can put in hydraulic lines it would make troubleshooting a lot easier. It is possible that yo have a problem with the control valve that would requiretaking it back to the dealer for warranty, the relief adjustments are more probable and easy enough for you to do and wont take more than 5 or 10 minutes to try.
I also suspect the reason for the hard starting now could be a fouled plug. If you have split 30cord of wood and more than an occasional stalling of the engine, I would check the plug and probably install a new one.