I hope someone with hunting experience chimes in, in case the rules are different for that environment, but when Kimber was about Leo's age, her off leash time was actually "leash still attached, dragging behind her." I had a very small chance of catching her when she played games like above, but I could grab or step on the leash.
Labs *love* the keepaway game, so it's also a good idea to teach Leo some version of "trade." Get a high value treat and start practicing having him bring you whatever he has in his mouth, praising him grandly, and giving him the treat. Start with things he'll willingly trade, and keep at it. Soon he'll be bringing you things just for the treat.
PS I don't think you're overreacting, because labs can get into dangerous stuff, and you need to train him not to run off with things that could hurt him.