Most presses have some sort of threaded adjustment screws on the top platen that allow you to adjust pressure. For flattening the print and/or dry mounting, the heat really does the work. You want the press to close firmly, but you don't want to have to force it, or you will get a crease if the print overlaps the edge.

The presses are designed this way so you can adjust the pressure and mount pieces much larger than the platen by using multiple passes. Use some old prints and adjust the settings.

Keep it consistent, too. If you set the pressure for dry mounting on 3/16 foam core, then use a piece of the same board underneath when you are flattening prints. Get some release paper for both processes. Always use release paper above the print; matt board can emboss the print.