Professor told me up front that she normally doesn't write letters for students who haven't done as much work with her
Suggesting that you write the letter and she will just sign it could be the professor's way to drive home the message that she does not want to write this letter of recommendation. I feel she is really unwilling to write the letter and probably hesitatingly agreed either because you were insistent or because she felt an outright refusal might seem rude. It would be better not to push her to do something that she does not want to. In your place, I would definitely look for another professor.