First off, let me say I am not a medical doctor. Your current caregiver's recommendation about amputating your foot may unfortunately be the best course of action to save your life. Choosing not to follow this recommendation and pursuing some other experimental course of action you've read about entails some big, big personal risks.

Having said that, there are other courses of action besides amputation you may wish to consider. The National Cancer Institute says about synovial sarcoma that "...Because synovial sarcoma is such a rare type of cancer, both adults and children with this disease are encouraged to consider joining a clinical trial (research study with people)."

Clinical trials are the way modern medical science advances and new drugs and treatments are developed. However, there are several things to remember about clinical trials. They primarily exist to gather scientific data for the good of society in general; they do not generally exist to help any individual in particular. There is no guarantee whatsoever that an experimental procedure will treat your affliction any better than existing treatments or indeed have any beneficial effect at all. Also, many clinical trials involve only half of the participants receiving an experimental treatment, with the other half receiving no treatment at all for comparison purposes. Thus participating in a clinical trial might very well allow your affliction to worsen because it is receiving no effective treatment at all.

If you are interested in participating in such studies, here are several lists of ongoing clinical trials which may be of interest to you. Cancer.gov lists 31 clinical studies underway for treating soft tissue sarcomas in general and ClinicalTrials.gov has an even bigger list of 109 clinical studies underway for treating soft tissue sarcomas in general, along with a shorter list of 14 clinical studies underway for treating synovial sarcoma in particular. Note that the ClinicalTrials.gov lists have a button called "Map of locations" that you can click to find those studies that are closest to you.

You are obviously in a difficult time in your life, and I wish you well in your struggle. Whatever happens, consider participating in a group like Sarcoma Alliance. Two of my cousins have suffered from breast cancer, one fatally and one still fighting it. They both believed it very important not to let their cancer spread to their smile. Reaching out to those who understand and share your tribulations can help. Good luck.