This is the configuration file I'm using: DsHidMini.txt (changed from .json to .txt to upload the file here on github)
This is the tracing results when connecting the controller via USB:

This is the result when connecting via BT (note that the "device specific" line is missing):

I'm pretty sure I wasn't running on this problem before updating the BthPS3 version (currently I'm using version 2.8.320.0). Will test if it's actually a BthPS3 issue somehow