Charge Registration fee but free downloads

No. I’d recommend you look at Restrict Content Pro and the Download Monitor Bridge:

https://pippinsplugins.com/restrict-content-pro-premium-content-plugin/
https://pippinsplugins.com/restrict-content-pro-download-monitor-bridge/

Gotcha. Thanks for the suggestions. Two more questions:
1) Using Restrict Content Pro can I add custom fields to the subscription form?
2) Do you know if these work with the Crowdfunding by Astoundify plugin which uses Easy Digital Downloads?

Thanks!

1). Yes you can: https://pippinsplugins.com/series/customizing-restrict-content-pro/

2). They will work with, meaning they won’t conflict, but they do not integrate with each other.