carpentrywood
I understand how one checks for square. But, what do you do when it's not square?
I put together four boards to begin forming a cabinet. I checked for square and nudged it into place. Then I screwed the boards together (using pocket holes). When I checked again, it was no longer square. Now what? There's no back board or cross piece to hold everything in place.
Have you considered one of the portable workbenches such as the Workmate?
They fold to a pretty small package and come in a variety of sizes and prices.
Black and Decker used to make several Workmate vises in a benchtop and toolbox version such as these
They appear to be discontinued. I found mine at yard sales, but they show up online occasionally.
If one of these suits, you may be able to continue to use your preferred tools.
Your idea is very similar to how hollow core doors are made.
If you feel a hollow core door is lightweight and sturdy enough for you, then I would say this approach will work for you.
Best Answer
Having screwed it together, and as importantly made the holes for the screws, you may need to remake one or more pieces of this frame, or choose new locations for the screws.
In some cases, one can put a clap across a diagonal of a frame to draw it into square if it is not racked too badly. Then new parts of the frame can help to keep it all in the desired shape.
Clamp it up carefully BEFORE you put in those screws. Make sure that everything is in its proper place and stays that way. A large part of doing fine woodworking well is in how much care you take in the small stuff.