I think when it comes to range of motion it is a case of "how long is a piece of string?"
Many people are quite happy with 110 degrees flexion and you already have excellent extension. But if you want to be more mobile that is another matter.
Has he told you about the risks and benefits of an MUA? You need to make an informed choice about this procedure.
Sitting on haunches as an exercise. Sounds a bit on the radical side if you do it in an uncontrolled manner. Going into a squat in a slow controlled manner where you are really using your muscles to work into that range of knee flexion could be beneficial.
Have you had physio for your knee since the op?