Paraphrasing the next paragraph: And you'd like to make object syntax not work for "everyone else".
Actually, no! :) Sorry to lure onto the wrong path with nebulous "various reasons", I've got nothing to hide! Reasons are: I want to use object syntax, not exploiting Perl's way of passing the object ref as the first argument.
Secondly, in fact, I would like other people's $self->frobnerize() calls to be routed to my Mixin, and I want them to use object syntax as well.
Hopefully, this has cleared up what I want ... and it looks like the trickery in mixin does exactly the, um, trick. Thanks to afoken who suggested this!