With over a 300 mile range with your truck, there is no reason to carry extra fuel for any of the main roads. Just drive on the upper half of your tank and fill up when you need to do so.
You will find two or three stretches of road where fuel may be about 110 miles apart. Teslin up to Jakes Corner comes to mind, with both being good stops for fuel and good meals at the restaurants if you are hungry. There are a couple more but with your truck range, nothing to be concerned with. Take a look at the "sticky" at the top of the Canada/Alaska section which I maintain and you can see the distances between stations. While some close, others may open. For a couple of our trips Pink Mountain was closed but the last trip, 2011, both sides of the road were back in business.