I'd like something like your current app, but effectively working like a site branded Pushover app instead. So it always redirects the user to their native browser (or browser of their choice) after tapping the notification. I encountered too many bugs in the in app browser when using your turnkey app.
It would effectively be a basic white labelled pushover style app, with default push settings setup by the admin, that can then be customised further by the user after installing it.
That way you can have a free app for users to install from the app store instead of users having to fork out $5 per licence for pushover.
All the cost is pushed onto the admin, that will hopefully up the install rate, you get native push notifications to the users device with no hassle or clunky signing up for other services and then associating accounts, and they get the full native web browser experience so all of your mobile friendly add ons work. Win, win, win, win.