Oh, poor kid. Please let her know, those nighttime highs are not her fault. Her hormones (growth hormones mostly) cause them. Many kids (my son included) become insulin resistant in the early part of the night and it causes their BG to go higher. I have to increase Eric's basal rate by almost 50% between the hours of 7 pm and 12 am so he will stay in range, and sometimes even that isn't enough. If he's in a growth spurt, he could shoot up into the 400s if it weren't for his CGM telling me about the high BG readings — I know this because some nights, if he's sleeping in such a way that the pump's alarm is muffled, I do not hear the alarm for several hours and I go in at midnight to find him at 375! But after midnight, his insulin sensitivity is greatly restored, and often even if I do not hear the alarm and correct him, his basal rate will start to bring him down, and the only reason I'll even know he went very high is because his CGM tells me. So that really could be the main cause of her bad a1c readings. But she needs to know these highs are absolutely natural! If her pancreas worked, it would put out more insulin to accommodate the hormonal shifts, but since it doesn't, she just needs to adjust her insulin to compensate. This is a learning process and it's very difficult for kids her age. Actually it's difficult for adults too!
Those highs at bedtime could explain much of the higher a1c, because they don't happen all the time and your random checks may miss the highest point. If a CGM isn't a possibility, and it sounds like it isn't, maybe what you can try is 3 days of checks every 2 hours during the night. You'd lose some sleep, but you could establish whether there were any distinct patterns overnight. Then, you could set her pump to increase her basal rate during the hours she goes high to see if you can bring her down into range. You'd have to keep checking her during the night after increasing the basal in order to ensure that you'd gotten the levels right (you don't want lows overnight, either!) but with some trial and error and checking regularly, you'd figure it out.
Oh, and one other thing she should know: it's not at all uncommon for teenagers to have high a1c's and poor BG control, even when they're careful about their diet and they always give themselves the right amount of insulin. The hormones play absolute havoc with BG, especially in girls when they have their menstrual cycle established. She is going to find herself getting very, very frustrated if she treats the Hba1c like a school test. She needs to try to take it day to day, making sure she takes her insulin and adjusts her insulin intake whenever she gets a pattern of highs, and LOTS of exercise is a must.