My only experience with a SAT phone as been one designed and hard wired into a 12v system. As an emergency responder I have not had a lot of satisfaction with some brands of rechargeable batteries.
You might look outside the BOX on this one. Knowing nothing anything about your phone will it accept one of these fast chargers?
http://www.energizer.com/products/energi-to-go/Pages/cell-phone-charger.aspxOr build on the concept.
Are you supplementing your battery with an accessory power cord powered off your snowmobile?
You might contact these folks and see if there COM people have any suggestions. They have people working in your environment. During the winter lay off the smokejumpers become trappers and find other employment.
Check the Alaska Fire Service for a phone number
Post the Model # and the battery you are using. I will play a long shot and contact a friend that spends a lot of time out in the cold and snow and see what he knows. He is also a radio bug.
After reading some of your post rather suspect you are ahead of the curve, and stuck with a system that does not work in extreme cold.
I was reading that the user should not fully discharge the battery before recharging. Is this a factor in the short battery life.