neat trick with the bag, I have a coats tire machine at the shop with a rim saver on it, but still mount by hand tire tools are a must never use a screw driver it does not have a curve lip and will slip, I use a towel (one my wife will not miss) start the first lip by hand and use wd-40 with my knees go as far as i can remember to push down at the starting point, when i cant go any more use the tire tool put the towel under it make sure you lip the tire tool on the rim this will not let it slip, little bites, repeat on top side.
One point i would like to make cheap tire tools are out there avoid these spend a little extra and get a USA made one and keep it in you tool bag for those trips good luck AL