I have a band aid solution to your issue which is annoying but it gets you up and running. I recently bought a One X and have the same issues as you but I have been getting by using the following technique. FYI my Galaxy S2 had the same issues when running the original ROM.
Follow these instructions carefully and your phone will get hooked up to the AppRadio, unfortunately you will have to follow these steps every time you turn your car on until there is a permanent fix. The following assumes you have already paired your phone with the AppRadio and have had a successful connection at least once, if you haven't following these steps will get you hooked up the first time as well.
Go to settings and go to the bluetooth settings, stay on that screen the entire time you are connecting the phone to the AppRadio
Connect the phone to the AppRadio and start your car.
The AppRadio should automatically start to try connecting to your phone, keep a close eye on your phone's screen and wait for the pairing request to pop up in the middle of the screen and quickly press "pair" , you only have about 1 second or less to press pair or the connection will fail.
You might see the pairing request come up twice, just hit pair quickly again and you will be connected and stay connected until you turn the car off.
The reason I say to go to the bluetooth settings first is because while you are on that screen the pairing request comes up in the middle of the screen, otherwise you have to pull down the task menu, press on the pairing request, wait for the popup the click pair and most of the time it takes too long and the connection completely fails.
Hope this helps, it's annoying but it lets you use your One X with your AppRadio.