I'm not sure what you mean by fiberboard and whether this goes on the top surface or underneath. Check where the mounting holes of your press will be on the top surface. I made a mistake one time when building a bench, and the press mounting holes fell in line with the seam of two 2x4's.
Also, it will help considerably if you run stringers around the legs a foot or so off the ground to give added stability. If possible, bolt the bench to a wall, the floor, or both. Strength and stability are most important. Also, make it bigger than you think you will need. It will fill up quick. The top surface of my benches are 2x6's covered with 1/2" plywood. Your idea of underbracing the top is a good one.