From experience, I say buy fake from snapdeal or paytm. Check it throughly for few days so that if issues arises, you can return or exchange it.
3k for new is not a good deal.
I also read about disturbance but don't know which way it is more clear - wireless or bluetooth.
I think its better to buy android on stick thn a bluetooth dongle.
Why dont you buy wireless headphones rather than buying bluetooth headphones?
I also want to divert my bravia sound to headphones wirelessly and did some research and it appears wireless headphones are way to go.