Hi Sharon, each patient and cancer is different, so is difficult to really say the best course of action, but being at a CCC is a must. They can do reirridation in select cases, I did 5x, and surgery is usually the first line of Tx for recurrences, like you're having with or without radiation or Chemoradiation.
There are many reasons for recurrences, due to field cancerization from exposure to carcinogens, being chemo or radio resistant due to a number of factors, the tumor was outside the surgical or radiated field, be secondary, synchronous or metachronous cancer, etc.
I don't see it mentioned, but was an endoscopy or pandendoscopy done of the upper aerodigedtive track for any other possible lesions, biopsies. It is sometimes done before surgery.
Most places follow NCCN Guidelines, but then it comes to a point that some are out of the medical books like myself, as my doctor said, and then it comes down to the experience and training of the doctor to be able to treat you or not. I changed doctors several times for various reasons, and will again due to my ENT and Radiation Oncologist leaving the hospital

Good luck