I had this exact problem on my DROID Turbo. I first called Verizon tech support. They had me to a factory reset -- no change. Then shipped me a new phone. I did a Google restore and same problem, RCS Phone services eating a ton of battery overnight and something keeping the CPU awake all night. Then got sent to Moto tech support by Verizon. Quickly escalated to Level III support. Had me factory reset with Automatic Restore turned off (it's a radio switch on the Backup & Restore page in settings.
That solved the problem.
I have been adding apps back slowly one or two a day and the problem has not returned.
Best Moto support can figure, one of the apps on the phone was conflicting with RCS Phone services and forcing the phone CPU to stay away ALL OF THE TIME.
I suggest you take a look at your battery use and tap the graph to bring up the second graph that shows what is awake on the phone (screen, WIFI, CPU, etc.). If you have the same issue I have, it could be something as simple as removing an app.
markbilek