I forgot that there's another (even cheaper!) technique for avoiding auto-focus noise: turn off autofocus! Obviously this does depend on having someone who knows how to focus manually, and is available to do it while shooting (if you're tracking a moving target), but a lot of auto-focusing is just down to bad set-up, e.g. someone waves an arm across the camera's field of view, so the camera pointlessly tries to refocus on the new target.
I don't know if synching externally recorded audio in post-production is within the "rules" for sweded films, but it's actually gives you much more flexibility in who and what you record. Single or multiple mics can be hidden in various places on the set, close to the actors, to give you the clearest possible audio without needing a boom operator ... but what you save on the boom, you lose on the mixing later!