Old Fart has some good ideas. Also try bike pants with better padding. I think a folding bike would be too slow for those distances. A more upright "comfort" bike would be slower, but less slower than if you had to give up cycling to work because it's too uncomfortable.

Also, if you have the bucks to drop on another bike, look at cyclocross and touring bikes. They have dropped handlebars you can use when you want to go fast, but they also have a more upright geometry.