by Dan Marsden.
you mention that you're releasing "your own version" of the app - which suggests you have some internal dev capacity?
Basically there's a setting in Moodle (not in the app, but your moodle site) that controls what authentication process to use. I assume it directs the user to a URL - you should be able to hijack that and send it to a custom login page that displays a link to your odic login or a manual moodle login page. (or you could customise your normal login page to display both OIDC or manual login options.
If you don't have internal development capacity, any Moodle Partner should be able to help you with this.
Good luck!