I try to avoid headhunters who think keywords matter (which, sadly, is most of them).

Exactly, I find it's just ticking off every item that's mentioned in the job description. Using the exact same words works best.

I find if you use PDFs it happens significantly less

Or they just get all the more butchered. Last time a recruiter was done with my resume, it looked so bad that I would've never interviewed me.

Unfortunately and apparently some recruiters have interns to convert those PDF's into their shitty doc-template. It happened to me a few times. Every time I had my CV ready and this seemed to help. Knowing LaTeX reflects very positively on you in some circles.