I really like passthepotatoes' advice.
The role playing part is still letting her know that you would prefer that she speak more often in her *regular* voice.
Curious about the shutting down intelligence and baby talk, my DD showed a very similar pattern in K. We resolved it by having her work at home(this year) at demonstrated academic level for part of the day and sending her to school for a few hours to do lunch, gym, specials, recess, etc.
Interesting, now that I think about it, the baby talk died down tremendously around that time. Hmmmm.....
Sometimes it's hard to remember how little they are because of how smart they are. Somethings, you just shouldn't *reason* with them, IMO. Better to just take control of the situation and manage it like PTP suggests.
As disturbing as the babytalk is, it's very likely that she will grow out of it and it's just a phase.
Neato