Letting the hate die down a bit would be the sensible thing to do. Then, promote her and show only the nice bits.
I'm sure I did dislike Tully in the beginning. All I ever saw was Tully bawling her eyes out and being too bitchy that early in the game. But the gods have endowed me a special gift: I may at any time change my opinion on anything and anyone.

Mikkayla was one of the HMs I was very fond of at the beginning but I'm losing patience with her because of her paranoias and petty issues.
Tully has grown on me because she doesn't appear to be devious and she sincerely seems to like Drew. She packed his suitcase when Drew took Ben to the PS - would Jade have done this? Tully does little things for Drew that are really sweet. She did admit to being an atheist... now this IMO isn't quite as clear cut as we might think and she mightn't be aware that she's actually an agnostic... but at least she had the guts not to be conformist. And she did tell Tim that he should really stay out of it when he didn't know what the convo was about. Extra kudos!
She does have an issue with, for lack of a better word, righteousness - the type of righteousness we are being brainwashed with every day. But because she's still inexperienced in such matters, she's not aware that she's waisting her time and should be focusing on other issues if she wants to make a difference in this world. Mind, at least she's thought about things other than fashion, shoes, hair styling and the colour pink. Kudos again.