Helps me a lot to have something already planned for the morning. Lately works well for me to have a book or magazine that is interesting, in the morning I fix maybe some tea and light food, then settle in with something to read.
I personally can't watch morning news, too triggering.
If I was in your situation I'd have to cut way back on coffee, maybe even eventually quit, at least for now.
Distraction might really help. I'd try a relaxing shower, maybe some gentle music, maybe a walk for exercise.