How to set up a white label licensing arrangement?

We have an app in the iOS App Store with a one-time up-front pricing. A company wants to license this app and offer it free or at a discount to their customers. Ideally they want a white label licensing arrangement i.e. our app with their branding.

How to do this, while retaining control of our source code?

We want to be able to offer a flat fee arrangement (e.g. $X per quarter), or a flat discounted rate per download, or tiered pricing (e.g. first X downloads / month: $Y, above this $Z) Both parties should be able to verify download volumes.

If we clone our app (with their branding) and either put it in the App Store as our app or give them the build and they put it in the App Store, can we restrict its visibility or availability to their users? If not, it will cannibalize our current app.

Apple's Custom Apps / Specific Organizations program may be an option but it says that "this option is only available before your app has been approved."

Thank you in advance for guidance and creative solutions.