Could be a little minor Dawn Phenomenon (DP) in action. Our livers have Attention Deficit Disorder and must have something to occupy them or they start misbehaving by dumping glucose.
Try eating a small, protein-ish snack before bed, like a piece of cheese or peanut butter on a cracker. Some DF members swear by a glass of red wine. This gives your liver something to do at night besides make more glucose. This has really, really worked for me, as does taking my exercise (walking) at night. I rarely wake up over 120-- usually it's down near 100.
Glad to hear your numbers are starting down in just a week on meds! Awesome! Good post-meal numbers, too.
Keep up the good work!