To all who chimed in to help (Thank You) and all of you who get to this thread either in curiosity or are facing the same issue at some point down the line (hope not), the issue has since been resolved by my AD's watchmaker.
When you flip the watch to see the movement, there is a small screw (visible from the caseback), which is just between the the first winding wheel and the crown. This screw goes into another mechanism / hook / clutch which in turn holds crown in place internally. In the case of my watch this very screw had come loose and this is what caused the crown to malfunction.
Prior to the fix, when I was demonstrating the issue to the AD, the crown had completely fallen off the case and was in my hand - I was simply unscrewing it and hadn't even got to the the time changing position and hadn't pulled it out at all.
During this entire experience the communication from the country manager here was way below expectation and he couldn't instill any confidence in me that he knew what he was talking about. I had made a video of the issue and asked him to share it with his technical team to get a high level discussion going and he didn't even do that. I had to request this before sending my watch in for 6 - 8 weeks (timeline mentioned by him) to people I didn't have much confidence in. The individual was very motivated to have watch completely serviced.
I've begun to see two things here:
1. Panerai is churning out watches and movements so quickly that they are not being able to test them appropriately and maintain consistent and reliable quality across the board. Are they biting off more than they can chew? The in-house price tag is a very lucrative spot to business in.
2. The staff in some regions is not up to the mark. I understand that not everyone working in the watch industry is as passionate about watches as some of us on these forums are. But at some point, if you've got to stop and ask yourself just how much of the industry are you being able to seep in and can you really deliver to your customer who is a passionate watch collector and a customer of the luxury watch industry. Callous and uninformed behavior at customer facing and senior roles is just not acceptable.