Kevin-
You've climbed more high stuff than I, but here's how I trained for Denali: load up a pack and climb something nearby. Start light, build the weight, and try to reduce the time. My nearby peak was about 2000' gain and I did a full load (70#) once a week and lighter loads once or twice a week. As a larger overall goal, I aimed for a minimum of 5k gain per week.

But one of my partners had advice that was really more suited for the West Butt:
"Based on prior experience, I recommend that your training include spending four days in a closet (around 44 square feet) with your pee bottle, pad, freeze dried food and climbing partner. It will also increase the mental training effect of this exercise if you have a tape recorded loop of the wind blowing on a tent at 75+ mph. If you survive the experience, the physical training for the climb will be easy."