It works fine when I commit locally (as yes, it's just a normal old git repo) - just via the web UI, it always uses the email in my github account marked as 'default' even though the repo obviously belongs to the organization, not to me.

If you haven't already, you should notify the kind people at Github. They respond within minutes, are friendly, and, most importantly, they actually react on what you write them. Who'd have thought?