Dear @campus2modify,
provided that the use of "virtual screens" is the best solution in terms of ease of coding and ease of use, by reading your post, that is to say the need of having a BT communication alive when switching between screens, I've tried to use the extremely powerful extension Itoo (by @Kumaraswamy ) that runs in background to manage the BT communication across two screens, and it works.
You can find my app and related Arduino code for testing at the following link:
I don't know whether it will hlep you, with your already made app, because Itoo imposes its rules (i.e. some restrictions on the use of UI and global variables) and it is probably more complicated to adapt your app to the use of Itoo rather than adapt it to the use of virtual screens, but it demonstrates that it is possible to maintain alive the BT client also when switching across Screens. Honestly until yesterday I was convinced that it was NOT possible to maintain alive the BT when switching across screens, but thanks to Itoo, i've found that it works.
Good luck !