Nice write up. I've done this a few times, but decided that next time I'm going to try to use another type of torch altogether, one that has a magnetic base and an LED head that can be set to any position, this would be better for bad situations like getting in trouble at the side of the road in the night.
Would be best to modify/remove the glovebox socket to suit something new, perhaps a USB socket or something- but it can't be LiIon as they are not stable enough- NiMH seems ok, though NiCd is better if you live in a cold climate. The trouble with all batteries is they don't like temperature change and only last. NiCd is by far the best for high diurnal range applications, especially the cold. Changing to NiMH gives you more capacity but less service life. Not sure I'll ever be keen enough to leave a Li-Ion battery in the car all the time. Here in Oz, a car can hit 90 degrees CENTIGRADE if left in the sun. Batteries, glues, rubbers, plastics, it all just dies.