I do the same. No food after 9. Necessary with gastroparesis, but that helps most everyone. Also, though not always possible, I steer clear of protein & fat heavy dinners. They take too long to digest. The lighter the meal, the better my fasting. In my case, what I thought was horrendous dawn phenomenon turned out to be gastroparesis.
I've taken a small correction before bed, half the usual dose. Know people freak at that, but I have to with delayed stomach emptying.
The other tweaking was the usual overnight basal fine tuning. I went up & down in half units. Kept the dose change the same for 3-4 days before making another adjustment. What works best for me is injecting basal right before bed. I take another Levemir dose 11 hours later. The worst fasting I had was using Lantus. Woke up either high or low.