Turns out they have an affiliate program, which is nice. I am not sure if they are targeting the long tail, which is where this tiny little self-indulgence belongs. Their process seems to assume that I own the domain where my site is located. Since I'm on Blogger, that is very much not the case.
They do offer me an alternative method of demonstrating my ownership of this blog, though. I cam put this into a post:
There you go, guys. Sign me up!