What is not bonding? Is it the print to the masonite, or is it the masonite to the soft wood. These are two different scenarios requiring two different methods.
If it is the masonite to soft wood. I have an issue with anything that calls itself a "universal adhesive" and would just get rid of the stuff you are trying to use. IMO this is code for won't adhere to anything. My standard wood glue is titebond. If you need work time they have one that does not set up immediately. I have had some issues with Masonite unless I rough scuff the hell out of it and even then it can be troublesome. I have never had an issue with epoxy coming undone. No matter what glue you are using make sure the surfaces of each board are scuffed and glue spread evenly. Some would say put glue on both pieces.
Just putting weights on the piece over night is probably not enough weight unless you are talking several hundred pounds. Get some clamps and cross pieces. For wide lamination I have used 3/8 steel bar as cross pieces when clamping.