My best understanding of the MWI's take on the Born rule is that the ratio of the number of branches for each outcome to the total number of branches gives you the probability of each outcome.

This is not the way the Oxford Everettians understand the Born rule. See the Hilary Greaves paper I linked to for a discussion of their decision-theoretic approach to probabilities in the MWI. This approach has its problems, but they are problems that the Everettians acknowledge and attempt to address (not entirely successfully, in my opinion). That's very different from Mark's attitude.

Also, the Orzel post you linked to doesn't seem to support your contention. Where do you see him committing himself to the branch counting appproach you propose? (EDIT: Actually, I see that there is discussion of the issue in the comments to that post, which is probably what you meant.)