The clicking when you swallow is most likely coming from your hyoid bone as you suspected. The greater horns can be shortened just as your calcified stylohyoid ligaments can be shortened/removed. There are several doctors who do hyoid bone surgery - Dr. Chhetri at UCLA Med Center in Los Angeles, CA, Dr. Dewan in Louisiana (she used to be at Stanford & Hyoid bone surgeries are her specialty), & Dr. Cognetti in Philadelphia, PA.
•Dr Dinesh Chhetri, UCLA, Los Angeles (ENT/ Otolaryngologist, Head and Neck Surgeon) Dinesh K. Chhetri, MD - Otolaryngology - Head & Neck Surgery | UCLA Health
•Dr. Karuna Dewan, Ochsner LSU Health Shreveport - Academic Medical Center - Specializes in Hyoid Bone Syndrome surgeries
•Dr David Cognetti, Thomas Jefferson University Hospital, Philadelphia 215- 955- 6760 (Has done many successful surgeries on members). Only removes ligaments if calcified. David M Cognetti MD | Jefferson Health
We have two members who just had hyoid bone surgery & are recovering - @a_catindisguise & @F_t. Here are a couple of links to discussions about it: