Large pieces like this, or even far bigger, are typically mounted in a big vacuum press under a rubber blanket. You don't stipulate what kind of print it is - fiber-based black and white or RC color etc. That's important. I'll assume you are referring to inkjet medium, which has its own challenges. But in general, a wet mount glue is generally used such as Seal Vacu-Mount or the current Daige equivalent. The skills involved are much like wallpaper hanging, and require practice. Lacking a vac press, you can use just a closed-cell high quality "weenie" paint roller to apply the glue, then a set of wallpaper brushes and rollers to get things flat. Expect to ruin quite a few trial runs; so save up scrap prints for test runs. Having the right humidity also comes into play.
When inkjet prints are involved, they should be well outgassed of any glycol, preferably a month or so, and the substrate itself must be permeable, and itself outgassed, thoroughly aired out, if you're even thinking of something like masonite or plywood.
I won't even go into cold foil adhesive mounting, the normal pro method these days - that requires expensive equipment and has zero tolerance for error.
There are pro spray adhesives which will work for this too, which I have good reason not even to specify, because they're proven to be very unhealthy and well as highly flammable, just like the hobby style art store spray you've already tried. These should only be used in a force-ventilated spray booth with an explosion proof fan motor, wearing a serious full-face respirator. I'm not exaggerating at all ! When these kind of sprays were popular in frame shops,
in the 60's and 70's, almost an entire generation of framers died prematurely in this country, and these sprays have been dreaded ever since. Permanent nerve and mental damage is also possible; I've seen numerous cases of that,
mainly in the insulation trade, which also irresponsibly uses these.
Masonite is bad in a number of aspects, unless for temporary display applications. There is a much smoother variety called Duolux available in 4 X 8 ft sheets. It should be sanded a little to give it more tooth. Art stores generally don't sell high quality fome core board either, although types of fomecore certainly are made in sheets plenty big for your purpose. It would be wise to mount on an oversized sheet of fomecore anyway, and then trim it down to size with a straightedge and knife.
There are speciality sources, especially for signage - that's where to look. Most only sell full packages, not single sheets. I can't go into many details here. The wisest thing would simply be to a serious frame shop already having the requisite equipment and experience. You might ruin any number of prints just in the learning curve.