Tawny,
Certainly looking for individuals who may be passionate about your alumni and willing to serve (as opposed to being arm-twisted) is a great idea. I might suggest actually targeting some graduates and staff members that you think might be good candidates. Frankly, people like to be asked. You communicating to them that you believe they would be a good fit, may encourage someone to agree to something they might never step up to do on their own.
June Gudeman