Hello,
the task looks very interesting, I would like to help you, especially in respect that you are a church, is a good feeling to do something important for the other people. We are a small family company from Cologne, Germany, offering about ten years web development on large projects - social , academical and health-care, so all work will be done legal, no moonlighting.
I have checked the polymer framework, have not had the opportunity to use it before - it looks very reasonable, we can good use it for the front end. For administration backend I would recommend a content management system contrex from a swiss developer company (is opensource), this system meets good your expectations to manage events and video/audio contents (I good know how is it from our church here). I hope on your mutual interest, it would be fine if you could please contact me to discuss further details.
Best regards,
Viktor Gotwig,
Cologne, Germany.