Have you tried an H shaped harness or harness jacket? It will take some time for him to get used to. You will need to put it on him for short periods of time when you can watch him in it. I have a cat that will walk on leash. He hated the harness at first but with multiple times a day everyday he learned that when he had it on he got to go walking. Now he can't wait to go. He knows when he sees me with the harness he is going on his walk. This solved the problem with him trying to get out on his own.
Repetition is everything with walking a cat. He needs to go on the exact same route everyday until he learns the rountine. I coax him to walk with a slight tug on the leash and a clicking noise. He knows it means move on now.