Okay, try using both the harness and the martingale at the same time. Attach the leash to the martingale and walk in the usual manner, ignoring the harness. Slowly transition to using just the harness.
When I walk my spooks, this is the set-up use:
Personally, I hate harnesses and do not think they are safer or more secure for the dog. I would never use one for the primary method of walking. When one of our 'Tzu's was diagnosed with a neck issue, I had to buy him a harness. I hated using it and the dog never cared for it either. I twas much easier to carry him around, :lol Of course, that is not practical with a greyhound. :lol