Any suggestions for sensible knots that would allow me to
a) tighten the loop around the screw at the bottom post-hoc and
b) adjust the length of the cord post-hoc (but it holds the weight of the boards + books)?

Why not have something moveable underneath to support it? That string seems impractical in general.

Yeah a piece of wood the same thickness as the shelf on a hinge attached to the frame could swing out and support the shelf. When folded in it would be the same thickness as the shelf folded up.

You’re going to find that edge and/or corner one night and you’re not going to have a good time.

Perhaps you could try a farrimond friction hitch on both ends? It fits a+b and it has a quick release

Maybe reverse the hinges so it swings down and out of the way. You might hurt yourself on the board sticking up when sleeping.

Doesn't that get in the way while sleeping? Don't you ever knock it down?

What I would do is connect it the opposite way round. So that it folds down, not up.
Give it a little leg that folds out when you pull it up.

The leg could be done in a few ways. But I would prefer it so that it is connected to the table top's underside on a hinge.
So, when the table is folded down the leg is tucked behind it, and when you pull the table up, the leg "drops" down and upright.

• The board is not supposed to go up while I'm sleeping 😅 it's mostly for cleaning etc (which is probably why I thought of folding up first). The hinges are a bit of a gimmick, not strictly necessary, but I really wanted the option to fold it in somehow, make it not stick out when needed.
• When folded in, it would be less in the way if folding down instead of up - but that would a) take away the space where any wooden leg/support could go while also b) making the cord solution impossible.
• A leg would indeed be a sturdier support ofc (and would provide a better justification for the fold-away feature). I'm thinking of adding one underneath attached to another hinge.
  However, I like the string for minimal use of material, and there doesn't seem to be weight problem with it 🙂