Morning readings are the slowest of all to come down, so don't worry about them. There's not much you can do, so I hardly ever bother taking them. Unless you have unlimited strips, or money, it's probably better using them to take readings 2 hours after eating to see what you can and can't eat. As a note, I DID find that if I ate and drank nothing from 2 hours before bed on, I got better morning readings. An endo told me that as a T2 on diet only, I probably "flat lined" dring the nght, so what i went to bed with I woke up with (other than Dawn phenomenon) Works for me, although I know some on certain medication regimes find a small carby snack at night helps. Try both, test, and see! Then you've done your best, so concentrate on the post-meal stuff.
Good luck.