Is there a gauge on there anywhere that might give us an indication of pressure? That little diesel may not be spinning that pump fast enough to get the volume you need for a reasonable cycle time. Most 2 stage pumps need to be spinning 2,000-2,500 rpm for max flow.
When you do stroke the cylinder does it move steady or does it move in spurts like there’s cavitation from a suction issue? How is the tank vented? Maybe you’re trying to suck a vacuum on it. Also the vent may allow crud into the tank. Most generally that spin on filter is the return side of things and there might be a coarse suction strainer in the tank where the suction line to the pump is.
How big is the cylinder? Like OD of the barrel? A tiny pump and a big cylinder may have tons of power but be turtle slow.
**edit**. In looking closer at the pics it does appear the way it’s built there is a filter on the suction side. That’s a no no in just about every hydraulic application there is. Pumps aren’t near as efficient pulling oil as they are pushing it. Look at store bought splitters up to large hydraulic excavators, the suction is a straight shot to the pump often fed by gravity or a pressurized system and all filtering is done on return.
If there’s ever a suction issue and a pump is starved for oil or cavitation happens downstream in the system is can do major damage. Not a big deal on splitter but on a large machine it can be stupid expensive!