I applaud your willingness to repeatedly dismantle and rebuild on the advice you're getting, Chris. It's our job to try and make all of this worth your while. Having a well-built
RMH work properly right out of the gate is as much
art as science, and some of the principles of combustion that we are exploiting may seem counterintuitive if you try to plug them into a conventional woodburner framework.
The consensus among those who have used a perlite/clay mixture as insulating infill (or to fabricate a heat riser, as I learned the hard way) is to make as dry a mix as possible. We make a moderately runny slip from fireclay and add just enough of this to a volume of perlite to make the grains stick together like a popcorn ball. If you overdo the clay proportion you lose insulative properties and it starts to slump and ooze all over (unless you're pouring into forms, which I don't advise either).
With your firebrick base, you could put down a layer of perlite and clay with a temporary frame around the perimeter, and lay your base on it immediately to key into the layer. Once it dries it will be pretty sturdy and the first few firings will vitrify the clay a little bit, making it harder still.