Aha! I think the issue here is that you're thinking of it in terms of two identical observers. The observers aren't identical in my arguments - one is post-hoc. I have realized where the discrepancy between our arguments is coming from with your example, because of the way I keep framing problems as being about the observer. Suppose I and a friend, Bob, are arguing about who goes in the house. In this case, there's not practical difference between our evidence. The difference isn't between me and other, the difference is between me and (other who I wouldn't have known about except for said experience).

Bob and I are identical (I did say this wasn't necessarily anthropic!) for the purposes of calculation. Bob is included in p(M).

Steve, who wrote a post on a rationality forum describing his experiences, is -not- identical with me for the purposes of calculation. Steve is included in p(O).

Does my argument make more sense now? Bob's information is fully transferable - in terms of flipping coins, he called heads before flipping ten heads in a row. Steve's information is -not- - he's the guy who flipped ten heads in a row without calling anything.

(ETA: I have no idea how to make them look right. How do you escape stuff?)