I don't have a solution, but I have had the same (frustrating) thoughts that you expressed.
It seems to me that there should be a "dry well" in the middle of the cooler. You fill *around* the well with ice, and put all your food in the middle. I have thought about trying to create something along those lines by putting a tall plastic box in the middle of my cooler - with clean bricks on the bottom to keep it from floating when the ice melts.
Haven't gotten around to trying it yet though.
Lang 48 Original
Superfast RED ThermaPen
"I love animals. I just love to eat them more. Fun to pet; better to chew." - Jim Gaffigan