This is entirely fair -- I agree! REST isn't a protocol in the same sense that HTTP is. Although I believe a protocol's semantics and encodings should be distinguished a la REST, a way to talk about a particular encoding would be a very nice thing to have.
>The "very loose definitions" largely stem from the encoding, not the modeling.
Sure, but the fact that we don't have strict definitions for common encodings means that you then have a discussion on it every time. It would be nice to have Standard A, that defines a common way to encode a common type of REST API (HTTP/JSON/etc) and we can just say our software uses that and REST is implied. Instead we get a situation where JSON-over-HTTP is perceived as being REST when it actually fails as a test in both ways. Some things are REST and don't use JSON or HTTP and some things are not REST and still use JSON and HTTP.