How, for instance, do proxies interact with these headers? I think that they should still properly serve from cache when possible, but I wouldn't bet the farm on it. Have you investigated this? And how's client support for this? Quick Googling reveals someone complaining about 206 responses not being cached by several clients, including Chrome and Firefox.
On top of that, putting range information in query parameters lends itself much better to HATEOAS. I get a URL with some parameters, I know that given a next relation all I need to do is navigate to that URL to get the next page of results. With yours, all I've got is you saying "these headers mean this."
Thoughts?