Miracle Muck in liquid form is not pH neutral, but only weakly so. It's a water based PVA glue. I still have mural sized papers prints mounted on Masonite with PVA glue from the mid 70's that show no ill effects attributable to the glue. So if that double archival whammy of Masonite and non-pH neutral glue have made it this far, I'm pretty confident in the process. I think the dried glue is not chemically active because of no solvent transport, and it also acts as a barrier to whatever bad stuff might be in the substrate. You can buy pH neutral Lamin-All or LaminAll from various sources such as Fredrix Canvas and UnitedMfrs.com, those work and smell and handle exactly the same as Miracle Muck.
Yes I have allowed glue to dry and then drymounted paper prints. Seems to work fine. One advantage to this process is that you can apply rather thick coats for porous or textured media like canvas and fine art papers which might give you a better contact that just drymount tissue. You can also reverse the mounting by heating the art package, then immediately peeling off the print. Have done that also, it works fine. The biggest disadvantage to drymounting canvas and textured fine arts papers is that it pushes down the surface texture.
I take comfort in knowing that if any of my glued canvases ever starts to peel up or bubble I can probably re-attach it with a dry mount or even on location with a clothes iron or tacking iron. Never had to do it though. I have a lot of glue mounted prints out there with zero problems relating to the mounting. OTOH a large percentage of my early adhesive mounted prints have developed bubbles, oozing at the edges, and de-lamination. Maybe adhesives have gotten better since then, but I'm not about to bet on it.
The basic reason for using Gator is its remarkable ability to stay flat when something is glued to it. For instance if you glue a canvas to regular foamcore, the package will deform into a dish shape and stay that way forever. When you glue to Gator, the package will buckle out towards you for a few hours, then flatten out perfectly. You can overcome the otherwise permanent warping of foamcore by simultaneously counter-mounting another piece of media to the opposite side, but that's kind of tricky and too time-consuming for my tastes. My recommendation would have to be for Gator. But for 1/6 the price at 8 times the weight, Masonite is also worthy of consideration. FWIW I have no recent experience with mounting to Masonite, so no pointing fingers please.