The type of machine used by chiro is called TENS machine. It just simply relaxing the muscles that causing your condyle to be compressed, which causing your pain.
Concerning the veneer proposal, I think that it is somewhat unreasonable. Just ask your doctor the basis for such proposed treatment which include any scientific study along with any peer review studies. IF the veneer is done right; essentially, it is no different than using the splint. The key is that if your doctor know where the condyle is. Have you taken any x-ray such as lateral ceph, tomogram etc. to determine if there is any skeletal discrepency. Typically, many people having TMJ problem is due to skeletal class II, the term used for having the mandible in retruded position which resulted in the condyle positioned in posterior-superior position. Good Luck