My first OSS contribution, before I could code, was a Bluecurve icon set for Rhythmbox that was merged into an ancient version of Rhythmbox on an ancient version of Fedora Core Linux on Jun 13, 2005. Your name stays in open source things virtually forever, and if you make it easy to find your email, recruiters hound you non-stop:
http://pkgs.fedoraproject.org/cgit/rpms/rhythmbox.git/tree/r...
Also, hiring managers, or decision makers (I could count myself as someone in this category) often do give a crap about OSS work. Give it a shot! Find a project doing something you enjoy and contribute to it. It doesn't have to just be code, documentation and graphics are also important (amongst other things).
The more opportunities = the more likelihood for a great opportunity. I'm always polite, tell them I'm not looking now, send me the job description and I'll forward it to my friends who are, reply to their email and tell them it's my preferred method of communicating.
Lets me build up a nice fat folder in Inbox of "jobs", filled daily by recruiters. I can skim it, see none of the companies I'm interested in, and click "done" on the whole folder. Takes a couple seconds, no skin off my bones, and the last time I was job hunting it meant my search took about a month to find something that really is a perfect fit.
So, why not spend a couple minutes a day dealing with recruiters?
You don't get cold calls. You plonk your CV somewhere, take a position and then have to change your phone number because they won't go away even if you have taken a position :)
Of course, I am not now not will I ever be in web development.