If you go with the timer you should recheck that timer to make sure it can handle around 700 watts.
I don't have the digital, but if you now have the digital, after the timer turns on the electricity going to the smoker, I believe you have to push the on button, and then adjust the setting? I don't know if the digital has a power interrupt memory which if there is a power interruption the smoker will restore the settings once power is restored. If so, you can setup the Bradley on the timer to run a couple of minutes, then have timer cut off the power, and have the third timer setting to turn the power on at one hour before you get up. You may want to do a practice run to make sure it will start to preheat when the timer turns on the electricity.