I've seen quite a few accounts of people with CCI also having jaw issues. Have you looked into Temporomandibular joint syndrome (TMJ)? Jaw misalignment can also be caused by AAI or CCI and this can itself create a whole host of painful issues.
Tight neck muscles can also be the result of ligament laxity, the muscles contract to overcompensate - not due to inactivity necessarily, this can be an indication of instability. My neck muscles are very tight and painful and I have CCI and AAI.
Does anyone find wearing a collar helpful? I tried an Aspen Vista but found it too uncomfortable. I may try a softer one but am concerned about causing further weakness.