You can root and run Safestrap without voiding warranty, as long as you are able to revert to stock if you ever need to send in for repair. Unlocking the bootloader will void the warranty because you have to do it through Motorola.
If I were you, I would do a factory reset because a clean wipe is always a good way to start a new version of Android. The built in battery stats does not really reveal much in what is actaully draining the battery. Check out this thread:
Read the first three pages fully so you can understand how Better Battery Stats works. If you are still having drain after a wipe, chances are you have battery-hoggin apps. You can do a dump of a log there and people will help you narrow down the cause(s).