What are the chances of one surviving synovial sarcoma?

IIt is not: A common dx, unlike its name, does not always occur at joints, but is lumped as a "soft part sarcoma" so it can metastasize to lungs, but unlike many sarcomas, it can also travel to lymph nodes. Resection free margins is key. Even 1 node conveys higher risk of relapse. Statistics don't help. You have a chance!

>50% likely cure: Assuming the tumor has not metastasized to the lungs, a majority of patients with this cancer enjoy long-term survival with today's treatments, which are evolving. Since synovial sarcoma has a trademark genetic defect, a specific "magic bullet" may be discovered as has happened for similar cancers. I admire your courage and wish you luck.