Well Centurion syndrome is an anatomical issue that is not very simplistic to treat.
Treatment would vary depending on
1. Severity of symptoms
2. Degree of anatomical abnormality
3. Whether your tear drainage pathway is normal and patent
4. Realistic expectations from the doctor as well as patient's side.
Next Steps
If you have established trust with your doctor (assuming you must have consulted an Oculoplasty surgeon/Ophthalmic plastic surgeon) you both should have a sit down and decide how to proceed with this.
when it comes to Oculoplasty surgeries, there will be variation in pricing from each surgery and patient because often the surgery is customized to the need of the patient and inherent problem.
Health Tips
Resolution of watering cannot be guaranteed. So your surgeon has given you correct expectations most certainly. Though a sincere attempt can be made to try and achieve that.