1. Background
You used to have a dispute A with another driver and his insurance. That dispute has concluded with representation by M.
You have a dispute B with the disability company, which is represented by G.
You have a dispute C with the former attorney M, you potentially might hire S.
2. Analysis
What you need is an attorney to represent you in dispute B against G, and your attorney will initiate a third party lawsuit to bring in former attorney M.
Your liability to disability company was caused by M's negligence. You want to make M (and his malpractice insurance) to pay the disability company directly. That's why the two dispute B and C should be tied together in one suit. Ideally in this case you won't have out ot pocket expense because M should pay the disability company and your attorney cost.
Whether S can do this, is another issue. I am not sure why he didn't suggest the third party lawsuit. My guess is this is too complicated because actual filing of law suit is needed and there are court motions etc. Maybe not worth the amount you owe to the disability company.
我隻是書本知識,一般認為執業律師有他的理由。