I'd think the usual way to handle that would be to die or croak to say the method does not exist. Is there something wrong with that?

I think this won't do what you intend it to do:

    (my $meth = our $AUTOLOAD) =~ s/([^:]+)$/$1/;
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Since you replace exactly what you match with what you match, $meth will just equal $AUTOLOAD.

As an aside, if you're writing an AUTOLOAD(), it might be wise to write a can() method to go with it too, if you haven't done that already.