I like the little details. And unlike Steve Gibson's SQRL--which I was trashing recently for being overhyped--you don't come off as a dick. ;)
Some questions/comments:
1. The github would be clearer (to me, anyway) if the protocol were written out in prose rather than in code. That may account for the following question:
2. It's not clear to me how the origin of the auth request is validated on the auth GET. I.e. how does the "relying party" (so to speak) validate that the SecureLogin client is following an auth link that wasn't MITM'ed by a phishing page?
3. I actually think the URI-scheme/browser-integration is a clever idea, and the UX flow seems fairly nice to me.
4. I think you're sort of kidding yourself if you say that lost-password recovery is not a big deal for big providers like Google and Facebook. For smaller providers, falling back to email verification is fine--or maybe doing nothing. Big providers offer all kinds of verification--email, SMS, domain-ownership, credit card--and a human customer support path. That doesn't change with TOTP or U2F, and wouldn't change here. Not a dealbreaker, really, but it's worth noting this weakness (lost-auth recovery) is probably here for the foreseeable future.
5. Having to enter your master password sometimes is a UX feature, not a bug--it teaches users to remember the master password. Just something to keep in mind on the client apps.