Here is how I use my 3-way:
Cool down on 110v the night before the trip.
Run on 12v while traveling
Switch to propane or 110 when camped, depending on if power available.
If I stop for lunch en-route, I switch to LP.
Sounds like alot of fiddling, but it's no big deal really. If I forget to switch for a rest stop, or lunch, it's no big deal really, as there is enough battery to cover it and you are going to recharge when you get back underway.
Interesting in the post above saying the 12v consumption is 15ah. How do you know this for certain, or where can I verify that rate?