Even though no one hired you to produce this show, you are allowed to put producing on your resume. The skills of producing are directly related to Project Management, and that should be reflected in your resume so you can leverage your hard work to potentially get jobs.
You created, launched, and executed a project.
You managed a team, dealt with a budget, and communicated with external vendors,
You had strict deadlines and dealt with group expectations.
Build this into a portfolio of your work on your website!
Other transferrable skills that can help you land similar jobs:
Managing vendor relationships
Creating and negotiating contracts,
Project Manager / Coordinator
Activity and resource planning
Organizing and motivating a project team
Controlling time management
Cost estimating and developing the budget
Analyzing and managing project risk
Managing reports and necessary documentation
What skills were you best at?
If you are not necessarily interested in those kinds of careers, take time to reflect on what came easy to you, and what might align with some of the larger goals we talked about earlier.
Did you manage the marketing or PR?
Were you good at fundraising?
Did you manage data input of audience/customers?
Did you work in customer service?
Find the skills you would like to continue working on, and try and leverage that for your long-term career goals.