I have a box fan on low 24x7 with a 12 on the input and a 7 on the output. That's not a HEPA rated filter set, but it's fantastic. Allergy season just went away (while in my room) when I started using it a few years ago. I also tried a 3 on the output, and that worked as well, but the flow was noticeably lower. The fan is cheap, $20. I change the filters every few months, and it always looks like I waited too long.

I used a cheap box fan and a furnace filter held simply by pressure differential.

Flow drops a lot, but it still works. Filter was dirty after some time. It was hilariously undersized for my purpose (serious belt-sander action leveling sub-floors), but air does move.

couldn't you easily test this by sticking your hand (wet it first) in the middle section of the filter and see if you feel any air coming through

You could, but I think the goal would be to make sure the design will work before going through the effort of making it. If you already have all the parts though definitely worth a try.