No problem, Stuart. You are allowed to summit the peaks from any trailhead you choose. The peak list suggests some of our favorites, but you are welcome to improvise. The one caveat: it should be worthy of the challenge. So driving up Diablo or Umunhum would not be in the spirit of the challenge.
Some people start with the suggested routes the first year, and then switch it up the following year. Others look try to make it extra challenging, or bag a peak as part of a multi-day backpacking trip.
Also note that the list of peaks has links to detailed trail guides for those suggested routes, and sometimes alternate routes. But consider those a starting point.
We have answers to this and other questions about the challenge in our support center.