What issues when quartering it. Wouldn't it cool much faster with the hide off and meat broke down in smaller pieces. Now with good game bags such as the TAG or BOMB bags flies and keeping it clean should not be a problem. I could see those old cotton game bags being a problem not breathing but the new synthetic take care of that problem.
The meat just seemed really susceptible to spoiling quickly when thawing it before cooking. I have noticed this on an elk and a couple deer.