First, how is average utilitarian defined in a non-circular way?

If you can quantify a proto-utility across some set of moral patients (i.e. some thing that is measurable for each thing/person we care about), then you can then call your utility the average of proto-utility over moral patients. For example, you could define your set of moral patients to be the set of humans, and each human's proto-utility to be the amount of money they have, then average by summing the money and dividing by the number of humans.

I don't necessarily endorse that approach, of course.

Has he been officially "impressed" yet?

I think Eliezer says he's still confused about anthropics.

What reading can I do on anthropics to get an idea of the major ideas in the field?

So far as I know, Nick Bostrom's book is the orthodox foremost work in the field. You can read it immediately for free here. Personally, I would guess that absorbing UDT and updateless thinking is the best marginal thing you can do to make progress on anthropics, but that's probably not even a majority opinion on LW, let alone among anthropics scholars.