What I have found to be most successful is to change the way the boosters organized for tasks (by the way, I use the same philosophy for my student leadership). In most situations there is a core group that does everything - same six people on each 'committee' and they just rotate who is in charge. What I push is that each committee chair is mainly responsible for getting other people to do the work. And, their committee should have no more than one other board member on it - preferably none. The best booster president I ever had did nothing. She got other people to do things. One of those that when brought an idea would say, "That's a great idea! Work out the details to present to the boosters." The worst booster president I ever had was the one that 'worked' the hardest. No one else did anything because she had her hands in everything.
The other part of this is that you have to get the fringe parents to buy in. Most are afraid of the booster octopus that they have experienced in the past - they help hand out cookies one time and suddenly they are ensnared and made the fundraising chairman. I push and communicate the concept to everyone, and strongly emphasize that I am not asking for anyone to help out more than one or two times a year - ESPECIALLY the new parents (how many freshman parents get so burned out that you don't see them again until graduation?). While some will do those one or two and be happy, most will end up doing four or five, or even becoming a regular.
This is not guaranteed as every community is different. As I mentioned earlier, it really comes down to the parent personalities involved. A well meaning, "I'm going to be the best booster ever," person can stifle everyone else. But the more you break the tradition that there is a core group that does everything, the better chance you have.