The best thing you can do to preserve ice and keep everything colder is put an added layer of insulation at the top. A couple of custom cut pieces of foam insulation work well, but even better is a flexible foam pad (like the backing on mouse pad) that can lay over the top. Then when you open the cooler you lift up only the end of the pad you need to access what you’re after. Here’s something we did to insulate your cooler.
The more insulation, the better. Take whatever material you decide to use for your cooler pad and cut to size so it fits snugly just at the top of the cooler. If you go for two layers, cut the inner layer in half and glue it to the single top layer. This makes a “hinged” lid so you only expose half the contents to that nasty warm air when you open it.