I would agree with most the above. Its not going to be about riding a high gear unless you have very low grades. Like .7%. Interval training is the best way to increase you speed sustainability, both on a bike and as a runner. I have not done any interval stuff on a bike, but after two weeks with 2 out of 4 days of running being interval training, I knocked off nearly 20 seconds a mile from my runs. Thats a huge improvement. You're body is probably more than capable riding faster and stronger than you currently do, what interval training does is informs your body that you will be using more effort for longer times and that it better get used to it. The ability to climb a hill efficiently is less about pure strength, and more about your ability to keep the ideal cadence for the ratio you're running.

For the hills in my area, which I would guess are anywhere from .3% to maybe 4% grades depending on my route that day, I like running 44/17. Makes it so that climbing hills isn't a pain, but when I want it to be I can make it more challenging without burning out by the time I reach the top. Also spinning helps your pedal stroke and subsequently your efficiency.