I feel like you and I are very similar in regard to our CML...we're both about the same age and started about the same time and we even have some of the same issues.
It was weird for me; the first two months or so I was fine, then I had two very big panic attacks; one that sent me to the ER (I didn't know what was happening having never experienced such a thing, so I thought it was the dreaded Long QT); and another that kept me up all night on a work night. Both instances were tied to having too much caffeine and then having a disturbance afterward; for me, the first time was too much coffee and a hot shower without eating, plus about to propose to fiancee; the second time was too much coffee at 8PM then being woken up an hour after falling asleep by a loud text message.
Since then I've battled anxiety and I have barely been able to touch caffeine. Anxiety built up and up, worrying about long QT, the diagnosis, being engaged, starting a new job, and so on. The point I'm getting at is that I never had anxiety during my life and then I was suddenly finding myself waking up in the middle of the night several times with a racing heart, whether I had a nightmare or not. It was scary. It has begun to subside (I'm even handling caffeine again now in small amounts) and I no longer really wake up from nerves or with a high heart rate in the middle of the night. However, I still find myself waking up about 45 minutes after I fall asleep. I'm not sure, but I think it could possibly be related to the Tasigna hitting the blood stream since I take it right before bed. I'm still trying to experiment but due to my schedule and the fasting requirements it has been difficult to do this.
That said, I would try a few things to try to rule out anxiety. A bit before bed I take a dissolvable magnesium supplement; this one is flavored raspberry-lemon. It helps with cramps and bone pain I've found, and you drink it warm so it helps relax you. Depending on bladder size though, don't drink too much before bed. Also, you might have to go to Bed & Body Works or something but get some lavender spray that you can spray on your pillow or sheets. This really helped me within a few nights of use. I have also found taking an after dinner walk alone really helps out as well. This has helped except for waking up within one hour of falling asleep, but this may be habitual. I just don't know how to break the habit.
Anyway, I bet a lot of it is anxiety related, as I've found. I have had good EKGs and I finally realized, regarding the Long QT (I bring this up because it was my subconscious fear), that if I'm not dead yet I won't be. And my CML results have been good. So I finally decided that I was tired of having anxiety. Once I did that it really helped my sleeping tremendously. Anyway, hope this advice helps you as well.