I have used many log splitters in my work as an arborist. I have had over six years of experience. Basically I am thinking you will have to buy some kind of hydraulic press part and tig/mig weld (fabricate) your own frame for your machine. I am not sure where you would find a hydraulic piston and engine for your project, but I could help you with design and how to as much as I am able if you would like. I think that any kind of hydraulic piston that is used for log slitting would be much more power then you would want. My previous boss that worked as an arborist (tree care, landscaping, removal) made his own log splitter and fabricated his own trailer and track for the wedge. I think the wedge part is fabricated by him as well. He fabricated both from "I beam" which is used in building construction. I think you would have the best results using I beam and machining a base. You will need some very thick welds on the machine. What you are talking about will work.
From what I gather, you want to make a vertical press with a metal base. You will need to buy a hydraulic lever and rubber hoses (the ones used for hydraulics that stand up to the kind of psi that a hydraulic piston puts out), a hydraulic piston and rod (high polished stainless), and I beam. You will need a Tig and Mig welder. A air compressor would be ideal, so you can use air tools such as a cut off wheel to cut the I beam. Then you will need a Drill Press, Belt Sander, etc. to finish the ends of the cuts to perfect. You could also use a band saw with a guide.
I would use 2-3 inch thick carbon steel for the base, and machine slots through the bottom of the base (maybe a router would work for this with a drill press or milling jig (for metal); so you can affix something to the base for a press. (like a makers mark stamp, or pattern for your steel). This can be affixed at a later time with nuts/bolts. The base itself should be flat and the sides should be affixed using nuts and bolts as well. Keep in mind that you should make the base long, not narrow, so you can keep your surface flat and level; your holes for nuts/bolts should be on the outsides of the base so you don't get marks from your press... If this makes sense to you. I should draw you up a blueprint of some sort.
The PSI's that a large piston puts out seems like a but much for annealed or red hot metal honestly, but it may be just right.
Hmmm..
Maybe a slightly smaller piston with slightly less PSI... I know my boss's wood splitter is an absolute monster beast. Let me know.
Goodluck. Keep posting. :thumbup: