Then use the space as you deem appropriate. If you still use it as an ice box, put your ice in buckets. Shop for rectangular buckets that are large enough to handle your local ice blocks (or several blocks), and most of the melt water will come out in the bucket. There will still be some condensation or melt water in the bottom of the box but the small amount remaining is easily soaked up with a sponge and towels.

That's what I do: I have a large built-in icebox under a cockpit seat locker with enough room for two large buckets (each holds 2 blocks of ice). On the top of the buckets we use small wire grids (made for the bottom of a bar sink). Found them in the kitchen section of a True Value hardware store. The grids sit on the top of the buckets to keep the food from sinking down and getting saturated in the ice water. We place items that must be colder down low on the floor of the box against the sides of the buckets, and things like lettuce and vegetables that can be less cold go on top of the wire grids, above the ice.

We average mid-high 40-degree ranges with this setup, with the thermometer positioned at the grid level (above ice, at top of buckets).