Are you more concerned about flex or scratches?

For scratches you really want something that adheres, like a skin. Anything else (like a phone case approach) will trap dust and dirt and simply grind it against the laptop.

For improving rigidity, I’d look into a 3D printed “case” for just the bottom half. I’d probably want ABS as it’s very rigid even when thin (though it’s been a while since I read up on current printing plastics).

If that case could be made to only have contact at the corners (so a tiny gap elsewhere) or fit over a skin, that could help prevent trapped dust from scratching.

This can be done, but will take quite a bit of effort, and won’t be cheap. Last 3d printing I had done for a phone dock cost me about $50, and I did the design work.

Edit: You could also glue on such a case using an adhesive like Goop - it’s very strong, flexible, but removable (I know, sounds like magic, but I swear it really does all that). Gluing at the corners then a dot in the middle will transfer stresses to the added case and across the laptop much better, making it more rigid.