2 large zippered pillow cases and go gutless and boneless method. Hide and bone are the 2 biggest hindrances to cooling meat fast and excess moisture is a great way to start the rotting process.
Water is full of its own organisms and streams this time of year are generally low and not super cold anyway.
Last sheep I shot was 8 days from hitting the ground to laying on the cutting board and never lost a pound of meat. Off the carcass, into a pillowcase single layer and layed in the shade on criss cross sticks, flipping twice a day to remove moisture from the bottom. Literally brushed off a half inch of blow fly eggs on more than one occasion, but not a single maggot ever touched the meat.