Lots of good advice here. There's about 5 homebuilts within5 or 6 miles of me, most are horizontal I or H beam with at least a 4", sometimes 5" cylinder. Two are vertical, all are tractor mount and run off the tractor hydraulics.
Volume is an issue on the hydraulic pumps, as is bending the beam, and pushing the wedge right off of it. Cut the beam and run the wedge right through to the bottom, and weld it all the way.
As for bending the beam, possible solution. I just aquired a "Walco" factory built 3 point hitch unit, 4x24 cylinder. (price was right!). The "beam" consists of two parallel rectangular tubes, and the wedge is welded between them at one end. The push block extends down beteen the tubes and has a plate across the bottom to keep it square and centred on the push. I've seen similar stuff for sale at TSC.
Four parallel pieces of steel (in effect) to resist twisting as opposed to one big one in an I or H beam. Seems to work really well, split stuff already that would have been bending the beam on some of the local "I beam" types. Trctor is supposed to put up about 2500 pounds pressure, would bet on less because it's about 45 years old and was poorly maintained before I bought it. Volume is a little low but gets the job done.
The 2 parallel tubes seem to work really well, light too. Food for thought.