I believe I see galvanized fitting in the plumbing. Therefore I believe the pressure is probably around 1500 psi, and a 4 in cyl, with a 2 in rod, will produce about 9 ton. Also, the pump seems to be driven on the flywheel end, and that is turning clockwise. So if you want to drive the pump directly, you will have to mount it on a pump mounting bracket, and use Love-Joy connections. Since you don't know the max rpm of the pump, and it was geared down to run slow, about 1000 rpm, you might have a problem with pump displacement. The engine might not be capability of driving the pump, because torque was achieved by gearing. Driven directly, you don't have that torque. This is all conjecture, because we don't know all the particulars. The newer Vickers pumps can run at 3300 rpm. A faster rpm on that pump will give more GPM, about 3 times what it is now, if the pump can handle the speed.
You might work out a new budget with new parts, and weigh the new parts with adapting what you have. A new 2 stage 13 GPM pump is about $130, and log splitter valve is about $60.00. mounting, $30 to $70. Love-Joy about $25., then hoses, fittings.