I mount paper andcanvasto gatorboard with miracle muck, I beieve you can do the same steps on masonite.
I cut the print, paper or canvas, a bit over the size needed to cover the panel. I cut the panel to the exact size I need to frame
I roll miracle muck on the panel, make sure you just cover it, not too much glue, here is a case of "less is more"
Position the print and roll a dry foam roll over it, then place the board flat with something heavy on it for few hours.
Trim the excess print around the panel and you are done
Hope it helps
Hugo