Braces for Open Bite and TMJ?

First of all, you need to understand that you have a very complex problem that if not handled correctly could lead to a much worse condition.  A comprehensive evaluation should be performed first.  The elimination of any adverse habits is critical (anterior tongue posture and mouth breathing are likely present, etc.)  Then, TMJ Dysfunction is a first treatment priority.  Your jaw likely has drifted posterior (most TMJ Dysfunctions have this characteristic) and will need to be repositioned into a healthy position for up to six months to achieve stability.  This can be done with a Neuromuscularly Balanced Orthotic which is worn on the lower teeth 24/7.  Then your upper jaw would likely need expansion (again, most anterior open bites have a narrow upper jaw). This can be done with a dentofacial orthopedic appliance (fancy removable retainer) The final stage would be braces.  With this approach, no surgery would be indicated and a very nice and stable result can be achieved. Watch my before and after section and I will post one of these cases (open bite, TMJ Dysfunction) for you to review.

Approaching an open bite in a patient with TMJ problems requires knowledge in multiple areas.I strongly suggest beginning treatment with a neuromuscular diagnostic orthotic and eliminating pain prior to initiating orthodontics.  The DNA Appliance is rapidly becoming the new standard of treatment due to its very low forces and ability to achieve orthopedic growth as well as orthodontic movement.These case can be complex and Oral Myofunctional Therapists can be a very helpful addition to the treatment team.Ira L Shapira DDSDiplomat, American Academy of Pain ManagementDiplomate, American Board of Dental Sleep MedicineRegent & Fellow, International College of CranioMandibular OrthopedicsChair, American Alliance of TMD OrganizationsThinkBetterLife.com

The major problem with anterior openbites is only your back teeth are coming together. This can cause some excessive wearing of you back teeth and pressure in you Temporo-mandibular joint leading to pain and discomfort. If your openbite is severe and related to excessive vertical development of the upper jaw, braces in conjunction with an upper jaw impaction can help to close the bite and bring your front teeth together.
If the openbite is not a jaw issue, but rather an issue with a forward positioning of your tongue during swallowing, than braces in conjunction with myofunctional therapy to eliminate tongue thrusting can also close the bite together. I do not have your records, but my gut feeling is you do have a skeletal issue in combination with anterior tongue thrusting and both would need to be addressed during treatment.
There are no guarantees that either treatment will eliminate your TMD symptoms, because there are others who have the same issue and display no symptoms. However, in your case, there is a good chance this will improve your symptoms. Remember, that stress is one of the many contributors to TMD symptoms and not necessarily bites.
I recommend you see an orthodontist and oral surgeon who both are well experienced in orthognathic surgery.