I like it! I should probably stick to bolting pre-finished parts together since it takes me on average 10 years to get one done. But...
I've thought about doing something like this before, not out of MDF, but like a skeleton frame of 1/4" SPF (Spruce/Pine/Fir - aka dimensional lumber) with a perimeter of harder wood (like ash) to take the bumps, skinned with 1/8" panelling. Perimeter being glued up out of a few large pieces and routed to shape, not bent.
I'm reasonably certain that as long as you have a solid space under the bridge and neck joint, and you have some full body thickness beams running between the two pockets, most of the area between can be hollow and it will still behave as a rigid body with gobs of excess strength remaining.