Hello @aj11
I’m not sure ‘native transitions between pages’ is possible with any wrappers. You can build your entire application with Jasonelle and using Bubble as a database & API. Native transition isn’t the same speed as Bubble page to page, unless you find acceptable a 2 - 3 seconds delay between pages. For Push and Contacts, it is available under Jasonelle.
When I looked your website, you seem to have already a working app.
" Control of the iOS and Android call UI for VOIP calls while the app is closed "
I haven’t the info how to setup this kind of behaviour. Let me know if you find out 
at 10 min. to build FREE 0$ native iOS/Android app 
. It’s sound like a push notification is required to be pressed to open the desired app.
Great web site.