Basil,
You are correct with your conclusion that the J-1 visa is the required visa if you plan to instruct in the US. Unfortunately, you will no longer qualify for the visa because you hold a FAA CPL and are considered "trained" in the eyes of the State Department. The J-1 Visa is designed for "untrained" individuals to come to the US, receive their training and then complete practical training by working as flight instructors.
Unfortunately, your choices are very limited at this point. I would also caution you of lawyers offering to "help" you file for work papers. Lawyers get paid for the actual filing of the application not the result and I have seen many pilots lose thousands of dollars in the process. Now does it never work…no there have been some that got lucky but its not the norm.