This is probably crazy talk, but I have been wondering how requiring people to slap a stamp on an envelope and mail in a résumé would go.
I think your idea is very elegant as everyone has access to the mail system, an actual stamp is pretty cheap, but it is just enough hassle to mail an application that it will filter out some of the spam.
The other suggestion I have had is that candidates need to hand in the resume in person, but I guess you could accept resumes from both mail and in person drop offs.
This might be a bigger lift than asking for a take-home project; if I'm expected to drop off a resume in Manhattan that's a minimum of a two hour trip for me. I'd rather spend two hours banging together a CRUD app to show that I can actually write code.
More than that, bots currently have no way of sending snail-mail :-)