Ok. Here's a version of BTSwitch that stay in the navigation bar at the top. There are two problems:
1. I don't have a device with MS BT Stack to test it with. It should work, but there's no guarantee.
2. For some reason, the installer refuses to register it in the Remove program list.
I can't figure out what the problem is yet. So you'll have to manually do it if you want to uninstall:
There are 2 files in the \Windows folder: BTSwitch.exe and BTSwitchSvr.dll, 1 shortcut in the \Windows\Start Menu\Programs. I suppose you'd have seen the shortcut.
Additionally there is a registry key created: HKCR\CLSID\{3E09681A-B124-42cc-8F61-255661C9DD72}, though it is not detrimental to have the key lingering around.
You may need to soft reset if the DLL is in use before you can delete it.
So, try it out and let me know the result.
Note: The program will turn off the BT when it is run.
Update: See my post down below.