I have three "extreme" coolers I use for thawing meat when I have several days. The two largest (70 quart) are labeled "5 day" coolers, my smallest one is a "3 day" cooler. Usually I'll put meat alone in the cooler overnight to start thawing. Then the next morning I'll add a couple frozen water jugs. The jugs help maintain cold temps, but more importantly are indicators of the thaw rate of the meat. I'll also put a Maverick probe hanging in the cooler about mid-level. Temps stay about 34-36F, plenty cold enough to safely thaw the meat over 5 days. I thaw 20-50 lbs of frozen turkey like this all the time.
The water thaw method works too, and is one I use quite often, but I generally don't change the water out like you read online. All you're doing by changing the water is adding warmer water to the meat to thaw it more quickly. As long as the water isn't frozen, heat from the water is going to transfer to the frozen meat. I'll put the meat in big Ziplock bags, then add faucet cold water to the cooler. Once you add frozen meat to cold water, the water temp will drop to about 34F. Since heat is transferred 25 times more quickly from water than air, it will take roughly about 18 hours for the leg quarters to thaw and you don't have to worry about the water getting above 40F. I'll check the condition of the meat after 12 hours, then every 6 hours or so. You'll know when the meat is thawed.