I know tor, in fact I run an exit node and do almost all my web browsing through it (including PM visits). Since the tor exit nodes are published, it would be fairly easy to disallow AM postings through them, or mark these posts as coming through tor. The same goes for most other anonymisers. Again, this does not strike me as something unreasonable, it would prevent AMs from posting from an anonymised IP address, but would not prevent logged-in users. Since there is no need to give any authentication when getting a new username from PM, this means that people can still preserve their real-world anonymity.

I though about including a passage on tor et al. in my OP, but felt it would sidetrack the main content of the post, and I could always explain that if somebody brought it up. Which you have, so thanks :-).