How about this -- you create a CFD application and assign it to a BLF on your phone. When the BLF is pressed the application looks at the last number you dialed (maybe we could make it smart enough to find the last "busy" call) and it monitors for when this extension has no connected calls. As soon as it detects the extension is available, we perform a makecall between your extension and the formally busy extension.
Since we will call your extension first, if you don't answer, the call will never ring the other party. But if you do answer, it will automatically call the other extension. The "acoustic alert" would be your phone ringing. You would know this was a call back by the caller ID on your phone which would probably say "MakeCall". This would require the use of a CFD application, the Call Control API, and a Windows service... but it is possible to do if you are willing to put in the effort.