I perfer a good recumbent for any distances > 20miles. I can ride my Strada ( http://www.bacchettabikes.com/jh-strada.htm ) all day without any discomfort. That would improve your speed and eliminate the back pain.
The second choice would be a touring bike. Make sure you are fitting on it correctly. A good fitting touring bike should be an improvement in comfort over the hybrid for longer rides.
Make sure you eat a good meal before leaving and drink plently of fluids even when it cool or wet. And slowly build up the number of long trips you make. Consider riding the full distance in the morning then taking the bus trip home or vice versa a few days a week. Then keep adding full distance trips as your stamina improves.
Craig