If you want something hardened and ground, a 3"x3"x1" jeweler's block would likely work, and they're available inexpensively.
I've used bearing races and similar things w/o issues. A jeweler's block is not going to be very hard; likely around 50 Rockwell C; that's about what is desirable for an axe. They're plenty tough for use in a press.I don't think hardened steel is a good idea for a press. Definitely not hardened through to the highest hardness. You don't want to create shrapnel.