I don't see any reason why you couldn't do it using the standard chassis. Someone might be able to come up with a reason this isn't a good idea... so wait for the pros to weigh in on this one:
1. Assemble the circuit board with the tube sockets in their normal position in the front/top side, but install everything else on the back/bottom side.
2. Decide where you want the tubes to stick through the top to decide where to install the board. The board will be screwed to the underside of the lid, so make sure there's clearance for the transformers, etc. Mark and drill the chassis lid for the board mounting standoffs and then mount the board to the underside of the lid.
3. Mark the tube socket locations, remove the board, and use a knockout punch to cut holes for the tubes to stand up through the lid. Use a good punch tool to make neat holes in the lid.
You'd have to use longer runs of some internal wiring to be able to get the lid on and off) but you wouldn't need to open it as often! Also you might try out different standoffs - by shorter or longer ones would make the sockets more or less recessed in the holes.
I'd just be careful to not reverse the pin order when flipping devices like the transistors from top to bottom of the board, but I can't think of any devices that couldn't be flipped easily. I flipped everything but the resistors on my VTA driver board (to allow for Roy's clear plexi cover) and had no problem.