Pairing to a module containing multiple Bluetooth units
You have 2 issues in here:

1) You want to communicate with more than 7 slaves. It's not possible for a master to have more than 7 slaves. However, it is possible for a device to be a slave in one network and be the master of another (called piconet). However, I have not seen any device that uses this (processing power would also be higher).

2) The issue of pairing the arduino automatically to a device, this is a software issue you need to solve in the app. The Android phone will detect 3 bluetooth devices. Since each has a unique identifier, you can have a simple algorithm to select one of them depending on the criterial, without user intervention.

In Bluetooth you must pair. This has to be done to keep both devices synchronized and talking. I think you're slowly going to the proprietary RF side. Perhaps you should think about your application and see whether you can use a non Bluetooth solution that can enable you to scale.