You also need to make sure that you have explained to them the reason they are doing Whole Brain Teaching. I find that middle schoolers buy in better if they understand the reasoning behind why you are using the method.
You can tell them that a really important thing to understand is that Whole Brain Teaching means less work for them, and that they will find it easier to remember what you are teaching than any other method, provided they give it a chance.
I would also address the petition. Tell them it is okay to have your own opinion, but they must be able to defend their reasoning. It is great that they put that much effort into what they want but they have not made their reasoning clear.
If they want input they need to address what it is that they do not like, but with the understanding that evidence and experience over years and years from college level on down has shown this method to be much more effective than most other methods. With that in mind "because I don't like it," or "because it isn't cool," or "because I am too shy," are not legitimate reasons to want to avoid Power Teaching.
Explain to them that it is okay to be uncomfortable with the method at first, but if they will give it a chance they will find it is really a lot of fun.
Explain to them that this method actually means less work, and less writing for them in general. They can only recall about 10% of what they read, and about 40% of what they both read and write, but 95% of what they teach to someone else (Dr. William Glasser's research)
Be up front with them. Find out specific instances and reasons that they think you are out to get them. Remember that a teenagers' perceptions are based on immediate, emotional, knee jerk responses, and they lack the capacity to make more objective adult decisions. Their brains have just not developed that way yet. They often do not understand that if you discipline someone it is not personal. Explain that they are each dealing with you one on one, but remind them that you have to deal with them as an entire group, one on (however many there are). You are not out to get them, but you must maintain a learning environment.
You might want to choose one or two who are leaders in the class and fold them one at a time into a class that is enjoying Whole Brain Teaching for a class or so. I would not do them in a class together.
It sounds a lot like a toxic grouping problem. Were they responsive with non-Whole Brain Teaching methods, or mostly skating along with little effort?