I'm thinking perhaps you could have multiple instances of the tag, each for a different purpose. Most tools would use the first one, but if it's something like a browser plugin it would just display them all to you and let you choose.
Yup. rel="logo-foo" where "foo" is optional and some set of standard subtags.
You could even consolidate this so you had rel="logo-favicon" and the favicon just become another aspect of your logo.
All that said, I think it's a solution looking for... well, not a "problem" really, because the problem is obvious. Rather, the whole thing seems like a solution to a problem that not enough people have. I'd wager the 2011 proposal would have gotten more traction and some format adopted if this were really a pressing concern.
You know what? What I'd like to see is some kind of de facto standard rel="foo" database that, a bit like the WHATWG, kind of becomes a place where you can submit rel types, spec a schema behind it, go through some semi-formal vetting and standardization process, and be able to crawl this information in a semantically-meaningful way (in addition to just researching the different types). It'd also be nice to formalize a migration path from a <link rel="x-foo"> as a prototype declaration to a <link rel="foo"> as a 'standard'.
