In my experience the best volunteer growth comes when the situation is attacked from multiple angles:
The usual suspects should be encouraged to help draw more people in. Yes, Sue is an excellent cook, but before automatically saying "yes" again, can you encourage her to think about who else might be ready? Perhaps somebody who's been assisting her? The head activity planner should be thinking about this too; he might not know who besides Sue would be a good candidate for cooking next month, but instead of just asking Sue to do it he can ask Sue for suggestions.
You can talk about this approach as a group, but it might not catch on until some people visibly do it. Get a couple head activity planners or usual suspects on board with the idea. Have the former publicly ask the latter for a nomination, and/or have the latter publicly say "hey, how about asking Alice instead? I think she's ready". Model the behavior you want.
Some people who could do these jobs would never put themselves forward -- either they don't think they're ready or they're reluctant to "take it away" from the usual suspects or they're shy. You'll never get those people if you don't reach out to them as I've suggested above. Others, however, would volunteer if they thought it weren't already a "closed shop", so you need to show people that it's ok to put themselves forward. At a meeting, instead of asking Bob to handle the decorations or Joe to organize the music, ask if anybody would be interested in doing this. You will probably need to do this for several months running; the first time you do it people will be surprised and won't have thought about it, so you may get no takers, but do it again. And again. Eventually some would-be volunteer will step up; when that happens, help that person be successful in the role, even if you have to grit your teeth a little because working with a new person is never as smooth.
Note: don't call for volunteers for a job that can't survive a beginner. But do choose roles that people would actually consider fun; I've seen groups where the only time they ask for volunteers is when they need people to clean up at the end of the gathering, and that's not very attractive to most people. That's not how you'll build engagement.
I used to be very active in a social organization that sounds similar to the one you're describing and saw these approaches work there. More recently I've seen it work in a community that meets weekly and has some specific jobs that need to be done each week. We've been able to get more people involved through a combination of asking specific people (who are not the usual suspects) and making open calls for volunteers.