If I remember correctly, you can record each track in Aum as audio without the need for Audio Share.
I’m a Mac user, and use iCloud for some of my storage. This is handy for me because AUM stores its recording in iCloud, so by default anything I record there is immediately(ish) available on my other devices. Same is true in reverse, I can export stems from Reaper into an audio folder and then have them available to the iPad.
Hope that helps, that’s as gar as I’ve gotten in my desktop / tablet workflow cycle.