Answer: Tape my fingers so they don't type RUN RUN RUN RUN RUN RUN.
Does she ever compliment anyone? Does that make others her trophies?
The kindness-phobia plus "major rift" plus the 12-hour silence on it equal significant issues. Just from your short description, I see two primary ones: the emotional injury underlying her deep skepticism of compliments, and the inability (unwillingness?) to communicate in an intimate way.
To wit: She apparently also hasn't told you anything about the source of said skepticism, even though it's unusual (insecurity typically fuels an excessive reliance on praise). Also, she wasn't able (willing?) to say on the spot that you upset her, but instead put you in the doghouse for the better part of a day without letting you know you were there.
My opening outburst aside, I don't think issues, even major ones, even major ones involving emotional trauma and inability to communicate, are an automatic deal-breaker. You "do think she's fantastic," after all.
However, her inclination to control what others say to her is a natural obstacle to speaking freely, and speaking freely is the heart of intimacy.
One possible conversation-starter is to center your argument on you - for example, by pointing out kind words she has spoken of you, and your confidence that her motive was kindness, not objectification.
Similarly, you also are entitled to ask how she would feel if you told her there was a whole category of statements you wouldn't allow her to make. My guess is she is deeply invested in protecting herself, and hasn't thought fully about what she's asking of you.
E-mail Carolyn Hax at firstname.lastname@example.org, follow her on Facebook at www.facebook.com/carolyn.hax or chat with her online at noon Eastern time each Friday at www.washingtonpost.com.