Mounting on masonite -
We did a lot of dry mounting in college. Standard tissue (MT-5 at the time) didn't always adhere well to masonite (maybe the surface could be altered to accept the adhesive).
Another product, which I think is still available today, was Fusion 4000. The sheet is very thin, and the entire sheet is a solid material, when used like tissue in a press (lower temperature, if memory serves), actually fuses itself to the print and substrate. I think this is how it works. This stuff worked on any substrate we tried, including foam core. It was expensive, though.
Our best success was in soaking the print in a weak solution of Elmers glue and water, then using a roller to mount it, allowing for shrinkage. I'm not sure I would do this with archival exhibition prints, though. We used it for architectural presentations.