If you've checked her night time basal rate (testing every hour) I would look at tea again, write down what she's having etc... But also along side this her activites for the previous 24 hours, as you might have a lag time hitting at it can be surprising sometimes which activity may impact on the blood glucose levels..
I would then compare foods eaten, activity to her night time readings to see if any pattern emerges..
A afterthought here
I know that you say that you've tested her basal rates overnight, they may still be out as she may have hit a growth spert or maybe had a reshuffle of the hormones as children do, they probably need more regualar checking of the basal correctness than an adult would