Participation inequality is a bunk idea.
Initiator inequality is not.
Most people are happy to follow the crowd and not risk social rejection.
Finding the people that are happy to initiate things (events, discussions, new ideas), put themselves up for acceptance/rejection is more difficult.
Build a list of people that have put themselves forward to do things within the group.
Most of the ideas will be bad, don't worry about that, let them know you always want to hear their ideas.
Soon they'll have an idea you can help them implement.