I like how you think. You're missing a bit of flow info for hunting, preserving, and living in the wild. 1st, your idea of refrigeration, using the water, isn't a bad idea, but it isn't needed and shouldn't be done since it can cause other problems.
The best way to do this is to begin before hunting. That is, choose the best methods of food preservation. In this case, jerky, biltong, & cold smoking meat are the best methods. To do that you need to build a rudimentary multi-chamber cold smoker. If you are in BFE without a nice bus, like he had, you can make a cold smoker out of limbs/trees/saplings, mud, (wattle & daub,) animal hides, etc. It isn't difficult and the rewards of doing it are well worth it.
Personally, I'd have made a lean-to shelter to live in then used the bus as the cold smoker. You can hang a literal ton of meat in there and smoke it for as long as it takes to cure it properly (far longer than you'd think). In fact, most of the info you can get online about cold smoking is modern-age cold smoking. Those methods use pre-preservation techniques as a crutch for short term cold smoking which produces preserved foods that can only last a few months. Proper cold smoking takes months to perform and the resulting food can last for years. Normally, you have help taking turns loading the fire box so it works 24/7. With a good design you can do it yourself.
Game is plentiful, in that location, so short term cold smoking would work well and push you from surviving well into thriving. In fact, you can couple short term food preservation methods like making small batches of jerky to gain a better overlap range for your food intake and food preservation. That means while the bulk meats are cold smoking, you can zone off your smoker for different temperatures for different styles of preservation, (Jerky making up front where it is warmer, cold smoking in the middle, biltong in the rear.) Only then you will go hunting.