My older dog despised the head halter and would do just what your pup sounds like he's doing. I'd tried a flat collar and a martingale as well. Our 2 most recent obedience trainers suggested folks use a prong or pinch collar in class to help train the dogs, the whole class used them which was 8-10 dogs. There are a fair number of folks on here who use prong collars on their labs, others who don't like them. Both of mine walk using a prong collar, both can sometimes still pull like sled dogs and they're 4 and 10 years old, but I know it can happen so I'm mentally prepared. See what your trainer's thoughts are on using a prong. Not all trainers like them and if yours doesn't and you really want to use one, you may need to find a different trainer. You could certainly stop in to a store where they sell prong collars and put one around your arm or leg to see what it would feel like on your dog. they do pinch but it's not like you're preparing them for the rotisserie.
I don't use a clicker- I never worked on it consistently enough for my older dog to decide it was a reinforcement worth working for I guess. My dogs work best for food, including on walks. I let mine sniff a fair amount. I got pulled down twice by my older dog when he was under a year old, once down a flight of stairs and once on the beach, I did a complete face plant. He likewise doesn't care about playing fetch, running after a frisbee or things like you'd hope your dog might enjoy. He would play soccer with me, kind of, although his favorite position was goalie. I think I ran more than he did but we had fun. I'm sure others will chime in on techniques for walking, it's a weekend and we tend to get fewer people on here.
I'd vote with your vet on the adolescent lab behavior and the use of prozac, although you have to decide what is best for you and your own safety. I'm not sure drugging him would accomplish the loose leash out on the neighborhood walk. They do reach an adolescent stage where all previous training seems to fly out the window. You have to keep at the training, trying to be consistent, and hoping this phase passes quickly.
Someone posted a link to an article on exercise and dog reactivity which might be of interest Exercise s Your Sit?