Suggestions needed in my tricky PhD situation
I'm addressing your particular goal of "I wish to change the direction slightly and explore more relevant techniques to solve the same problem I am dealing with".

One particular suggestion is to use a kind of "red herring" strategy: Work on two directions in parallel. The one direction is the boring/phony stuff that your supervisors want you to do, and that you will mainly discuss in meetings, thus giving them the impression that you buy into their game. The other direction is the direction you actually want to follow. The time to first mention this direction is when you have made some substantial results - you may then calmly announce that you plan to submit them to a specific conference.