Although MDF is flat from the factory, it can/will sag over time if not well supported, and especially if moisture is allowed to penetrate. This is one reason many laminate two 3/4" pieces, and then further laminate both sides with Formica. I used two pieces of 3/4" phenolic BB ply for mine, laminated using contact cement (about the only thing that will stick to the phenolic surface).
Hinging your RT to the wall can save space, but can also introduce other "issues". The play in the hinges, for example, may introduce some tendency toward vibration, which can affect the smoothness of cuts. Some sort of bolt-down flange in the lowered position could solve that problem, though.
If you use 2x4s for the edging around the MDF, you could cut a wide enough rabbet for the surface to be flush. Then, "1x2s" could be used for additional (glued and screwed) under-table support, if you liked. I'd keep them a couple of inches away from the plate opening, however, to allow better access to the router. That might be different if you use a lift, however.