So here's what I did:
First, I removed the top cover (where we usually put God idol etc). Then, I removed the three holding screws that keep the music system in place. There were two more screws on either side, and I didn't know if removing them was necessary, but I did so anyway.
Then, as per jaggu and Audioholic's advice, I applied some real good force while trying to pry out the holding clips and with some considerable effort (I was scared to a point that I was going to break something), the entire assembly popped out. I checked to ensure that nothing was broken and indeed, nothing was.
The panel is tethered to the car by three cables:
1. The power supply to the system
2. Wire harness for speakers
3. Hazard light button wires
I detached the wire harness and hazard light, but the second cable was not coming out. So, I just left it in place and perched the assembly on the dash.
Looking through the gap thus created, revealed an open space leading below to the foot well. I routed the two wires in question (Aux cable and Bluetooth head unit cable) through this space, dropping the power adapter and wires into the driver's side foot well.
Now, I connected everything and checked that the system was working as expected before pushing the assembly back. It locking in place with a reassuring click. Then I replaced all five screws that I had removed, and snapped on the top panel.
I used double sided 3M tape to then mount the Bluetooth unit on the dash at the desired position.
I took the power adapter and inserted it into the DC 12V socket, and rolled up the extra wire, taking up all the slack and tucked it away in a recess that I found below the OBD port. This was then blocked by electrical tape, securing it in place and blocking it from view.
Now for the final setup:
The Bluetooth unit I'm using is a Kinivo BTC450 with A2DP and AptX support with a built in echo-cancelling microphone. It is powered by a DC adapter and powers on when I turn the key (basically, just like the built in music system). It feeds into the Aux port of the car and streams both music and calls through the car speakers. I chose to go with a DC powered unit instead of one with a built in battery as I wanted something that would turn on and off with the music system itself and not drain battery while not in use. I also didn't want the hassle of charging the unit (as is the case with some devices with built in battery). Another advantage is that the power adapter comes with a built in 1 Amp USB charging port, so that I can charge my phone while it's in the dock while also powering the Bluetooth unit. Among the options available with these functions, I chose this particular product because unlike other units like Belkin, Soundmate, etc. (which require you to press the button on the unit and pair it manually with the phone every time you enter the car), this one goes into auto pairing mode the moment it powers on. So it's fully automated and no user interaction is required at all.
My phone is mounted on the centre console using an iOttie One Touch XL mount onto which I have stuck an NFC sticker, programmed with Trigger to launch Car Mode, fire up Car Dashdroid app and turn on GPS Location and Bluetooth. It has a button that releases the spring loaded clamps as soon as the phone is placed in the cradle and these securely lock the phone in place. When I want to release the phone, I just press the release buttons on the side and the phone pops out into my hand.
I use a Galaxy Note 3 as my phone, and I use Trigger pro, Tasker pro and Secure Settings pro to help with the above-mentioned automation. Another neat mod I have done is using Xposed framework modules, I have set NFC to listen even with the screen locked.
So now, when I get into the car, all I have to do is to touch my phone to the cradle. It auto-locks into place, the phone reads the NFC sticker and goes into Car Mode and Bluetooth get turned on automatically. When I turn the car keys to either acc mode or ignition, the DC power fires up the Kinivo Bluetooth unit which auto pairs with the phone without any additional user input. This triggers the launch of PowerAmp Pro on my phone and music starts playing from the car's speakers. When I get a call, the music fades automatically and the caller's name is announced. Since the phone is in car mode, all I have to say is "Answer" or "Reject" for call actions. I can also do that manually by pressing the Kinivo's multi-function key, but voice operation is much cooler and safer, as I don't have to take my eyes off the road. I also use voice commands to trigger Google Now to make calls, navigate, etc. as I have set Google Voice Detection to always listening on any screen and respond to commands issued via Bluetooth. Finally, the exit strategy: when I turn off the car, the power to Bluetooth unit dies, thereby disconnecting Bluetooth from phone. This is a trigger for the phone to exit Car Mode, turn off Bluetooth and location and return to phone mode.
My car is now fully automated as far as integration with my phone is concerned. It has all the functions any luxury car stereo had and the best part is that it'll never be redundant as I can keep adding features via my smartphone.
The setup is minimalistic, clean and relatively wire-free and I am a happy, happy, happy man.
Showed my setup to a colleague and my wife. Both were blown away!