Oh man, this this THIS! I'm also a big guy, but I spend many hours of the week strength and cardio training in the gym. My health is better than the OP, but my muscles are GREEDY for air, and I was lucky to get 40 minutes out a 80cf tank. Then on a dive in the Keys a DM asked if I wanted to try a 120cf steel tank since I have the strength and size to handle it easily on deck.
Couple things happened:
1, I looked like I had a water heater strapped to my back, and immediately got the nickname "Rheem" for the rest of the day.
2, because I was not stressed/worried about being a gas hog -- and putting a limit on my smaller lung-ed partners' dive times -- my breathing became far more relaxed and calm. I used far less air for the same amount of time at the same depth.
3, because of the heavier steel tank, I needed less trim weight and bulk in the water. I was far more streamlined, less concerned about adjusting my BC, and conserved more air.
4, I realized that there was very little to see at +100' other than my own ego. Staying shallow and calm made me a magnet for turtles and pufferfish. Win win.
I know my gas consumption problems are far different than the OPs, I wonder if the same solution (bigger tank) would be the most simple and appropriate?