I've done plenty of mashing in my granniest of granny gears. Some of the places I ride are similar to the area around Lisa's home. I *try* to spin up in the beginning of a long or hard climb, but I could never be spinning at 100 rpm! My usual cadence is around 80-85 and I am sure I get down to 50 or 60 on some of the 15-20% climbs around here. I just did one of those on Sunday and on the hardest part, I was mashing and praying I would make it. Like Lisa, my average goes way down on those kind of rides and I don't care. When I saw your average, Mr. Silver, on a century with 8500 feet of climbing, I was astounded. I can make it up those climbs, but I am simply turning the pedals over and not thinking about anything except getting up the hill. Trying to go fast on steep grades just isn't going to happen for me. I can and have improved my climbing speed on shorter or less steep climbs, but at a certain point, I can't do more. I just don't have the strength.
At one point, I almost got a compact double. Shortly after that, I got my new bike and ended up changing out the 11-25 to an 11-27. I am really glad I have a triple...