As I already sent by mail, I could not find much in the log, in fact it was more or less empty. Recently I heard from other people that they have Bluetooth problems with CM11, but the same configuration works for me, so I don't understand what's happening. There is only one strange output: The "socket creator" is null, which is nearly impossible. Does the app show an error condition?
Perhaps I explain how the pairing process usually works, at least for the VW "Premium" device, it looks like the Audi behaves the same.
First the car queries the phone's available profiles. This may happen as soon as Bluetooth is switched on in the phone. When the car detects the SIM Access Profile it chooses the higher security pairing option with a 16 digit PIN entry (or 6 digit PIN confirmation with newer devices). If the car offers a 4 digit PIN, it did not recognize the SIM Access Profile, which means my app is not properly started. Your car does not ask for a 4 digit PIN for the Handsfree connection, I guess it still has the 16 digit PIN from the initial request.
After you enter the 16 digit PIN the car starts talking to the phone using rSAP. If something unexpected happens inside this communication the car may abort the rSAP connection and fall back to using the Handsfree profile. If this happens the Bluetooth part of my app is usually working fine, but the SIM card is causing trouble. Problems of this kind should be visible in the "main" log, which was empty in your case.
The PIN dialog on the phone at the start of the rSAP communication should not have any effect on the connection, it happens to me every now and then and is probably caused by a racing condition. At least it shows that an rSAP connection is requested by the car.
Can you please create a "HCI" log, either with my logger app or from inside the Android developer options?