A-ha!
The problem turned out to be that MaxPoint didn't have the permissions access the C:\Program Files\Diffraction Limited\MaxPoint directory (even when I ran it as the Administrator user). I just added my user's account into that directory's permissions list and propagated it down the tree, so it now works. (Thanks for your suggestion which was on the right track anyhow.)
The auto mapping feature is now doing its thing - *much* easier than manually slewing / plate solving / syncing each point by hand!
