Sounds to me like a standard Polar Bear 48 cooler would do the job perfectly. Freeze the meat for at least a week and it'll stay frozen for days. If you're worried about opening the cooler too often, fill it up with ice when you begin taking food out - even if it thaws it'll stay plenty cold.
Dripping water is not an issue with a PB, anything wet stays inside. Once a day open the zipper an inch or two and tip it so that any meltwater runs out.