Since we're talking about presses.....some things popped into my mind that I feel are very important....
When installing dies on your press, leave them a bit loose, that way they have some "wiggle" room to move a bit with odd/uneven shapes in what you're forging. Another reason is that dies, as well as some portions of the press will expand/contract when heated/cooled. If tolerances are super tight, things can, and often will just break a weld or even part of the press structure.
If there is one thing that will hard break dies and/or a press, it's not having/allowing enough "slop" in either!
When it comes to actually building dies for your press, don't get too concerned with the steel you use for dies. I would recommend using plain old A36 cold or hot roll.
Why? Way back when I first purchased a press, I spent a substantial sum of money buying D2 steel for dies. I spent the time and effort to not only cut/shape pieces of D2 to what I needed, but also heat treated them, thinking to keep them from deforming during use.
DUH! Soon they were all back to dead soft and deforming, because the heat of forging had tempered them out to dead soft. Ever since, I just buy A36 in the shapes I need, and lightly tack weld the pieces to the dies plates...... that way a quick pass or two with the angle grinder and the old deformed ones come off, and I tack weld new pieces in place.