Hope the post's not too old!
But, I've got a video for their hair issue. I decided to make it after getting TY Twilight Sparkle & she was really frizzy. I like her face shape better than BAB, but their hair is very similar. I think TY's is a little less thick/stiff per strand. However, the method works for both BABs and TY. They frizz up when kids put them in the bed and don't bind the hair first. Then it gets tangled/messy and they pull combing it out and it frizzes.
I made it because I don't think there's another specific plush de-frizzing video anywhere on YT, but tons of people could enjoy their plush more if the hair could be restored.
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I hope this can help your plush too!