Well Heck Tom, if you can flat weld, doesn't have to be any vertical or overhead beads welded, just roll that frame around so all welds are flat and go for it. Grind the old welds out, put a Vee in them to get better penetration and build up a nice big bead. Do a bit of looking around and see what size welds are needed. and for sure go over all the old welds that are holding and make them larger. Best would be to actually grind them out a bit to get good penetration into the I-beam.
As mentioned above be SURE to support that bottom die holder with a long support, if not all the way to floor, at least down the vertical leg so that butt weld isn't carrying the load. There is too much good steel in that frame to junk it. Don't forget the top where the cylinder support attaches, that needs to be re-enforced some also. I think I might consider adjusting the control valve for 2,000 psi max for 20 tons. Maybe even 1700 psi for 16 ton or so. I'm concerned about that single vertical I-beam for support.
You got a nice project ahead of you