Hi Derek,
I see a lot of different TMD at my clinic and I would look at the following.
First, what is the upper cervical like? If the upper cervical has poor mobility needle greater occipital, sub occipitalis, C2 and C3 paravertebrals and greater auricular homeostatic. If there is a lot of upper trap tightness too get spinal accessory homeostatic because the upper traps insert at the base of the skull. Follow this up with a lot of upper cervical ROM, and retraction exercises.
Second look at how his jaw is opening, a lot of times there is severe lack of protrusion which limits the necessary anterior translation the TMJ needs while opening. This will be limited when upper cervical is in more extension (forward head posture). If he is lacking protrusion severely needle the suprahyoids. Needling the masseter is always helpful in addition. In the advance course they teach needling the medial pterygoid which would be helpful for this patient as well.
If it looks like there is trigeminal nerve damage from radiation make sure you are doing a lot of opening exercises with end available range isometrics to help restore this strength.
This patient may need additional manual therapy internally as well to get the areas that you are not able to dry needle.
Hope this helps!
Dan Price