The list_of_elements_of_multiplicative_group should definitely return elements of R, not Python integers. Somewhat ugly, but ok there is your group:
sage: M = map(R, R.list_of_elements_of_multiplicative_group())

Now the isomorphism with C2 x C4 is not unique, so its not clear how this can be improved. Maybe one could return a particular morphism from C2 x C4 to R. In any case, as far as I know this is not (yet) implemented.