wall thickness and infill density.

As far as price goes - decent flexibles are not cheap. Just how it is.

You can have a look around for flexible pla. I've got some cheap red stuff. Pretty stiff but would probably work for you.
Basically the cheaper flexible pla is the stiffer and weaker it tends to be.
But worth a shot as you can usually buy a smaller reel.

Sunlu is the cheaper stuff I have. pretty cheap - ish. https://www.amazon.com/SUNLU-Filamen...ible+pla&psc=1
one of the advantages of flexible pla is that you can print it on any surface and don't need to heat the bed. Sticks like a limpet, but is easy to peel off. I wouldn't print it on blue tape, probably tear the tape. Everything else should be fine.

The sunlu stuff is pretty stiff but also very strong - so would probably suit your purpose a lot better. $22 for a 500g reel.
Also stiff enough that it will print on any 3d printer.