I wonder why you'd complain about plateauing at 13.5 mph on a commute? You don't even have enough time to warm up properly and if you're feeling tired and needing to recover after you've plainly been pushing harder than you should.
For 5 mile trips average speeds of 12-15 mph on an unloaded bike are common. 6.5 mph hills are just that.
Here's a suggestion - if you want to improve your speed and strength join your local bike club that has a group that you like. If they're a little faster than you it will egg you on.
As for your commute - good work and you'll find a great deal more benefits as time goes on.