I've always had pretty basic coolers, but there's some very effective ways to maximize their efficiency. The best thing is that these tips will work on any cooler, no matter the quality.
PRECHILL: I often only use ice for the pre-chilling of the cooler. That is a crucial step, don't omit it. Using a saltwater slurry will lower the temperature a bit more. If it's an option, you can also put the cooler in a walk-in freezer (or leave it outside if you live in a cold place) overnight before packing.
PACKING: When it comes to packing the cooler, instead of ice, I mostly use freezer packs. We get vaccines and some medicine shipped cold, so we always have a ready supply. They are available commercially, you can ask your vet to save you some, or make your own. I haven't tried the last option, but I think they're just salt water. There's discussion on the google.
Whatever you pack the cooler with, make sure that your ice or cold packs are super chilled. A regular ice machine is only cold enough to freeze water. I run my household freezers much colder than 32F, so any ice or freezer packs that I use will be much colder than 32F when I start packing my box. This makes a big difference.
The exception to using only cold packs is when I need maximum duration from the cooler. If that's the case, I use ice cubes to fill in the gaps in the food after I've finished packing the cooler. The more air space there is inside of the cooler, the less efficient it is. This holds true with your refrigerator and freezer as well, mine are always full, even if there's not that much food in them. I sometimes fill them with water bottles, but always have a bunch of the freezer packs in the freezers.
I make sure that the bottom and sides of the cooler are lined with the cold packs, so the food is in the middle, then a layer of the cold packs, then the wall or bottom of the cooler. I also make sure to surround things like dairy products with more cold packs or ice. I layer more of the cold packs on the top of the food.
So that's the loading portion. My coolers are seriously heavy when I get done filling them. That means maximum efficiency.
EXTRA INSULATION: the next, and just as important step, is to add insulation on the top. Camping stores and places like the outdoors section at your local MalWart will have the mylar emergency blankets. Open one of those, fold it loosely to about the size of your cooler, and drape it over the top of the food, tucking in down and trying to completely cover the inside of the cooler all the way to the edges. You can also use mylar lined windshield sun reflectors like you use on the dash of your car in the summer (at least here in FL, I consider these essential). They're even more efficient than the emergency blankets, but take up more room. I often use both if there's room.
BE EFFICIENT IN YOUR USE: Finally, use some common sense. Stay out of the cooler as much as possible, don't open it up and browse around. Plan what you're after before opening the box.
COOLER PLACEMENT: Avoid, when possible, leaving it in the sun or a hot car. Mine's usually used in a car or truck, so it'll be wrapped on the top and sides or at least covered with a blanket or two. As the ice melts, NEVER drain the cold water from your cooler unless you don't need more than a few more hours from your cooler, since once you drain the cooler you've lost most of the thermal efficiency. It'll warm up pretty quickly after that.
I can expect to get at least 3-5 days of really cold storage using these tips. That is, cold enough that the ice hasn't started to melt. Especially when I use my cooler for only transport and am not opening it much instead of working out of it, it's not unusual for me to find that none of the ice cubes have melted after days in the back of my truck. I've brought frozen fish and game home from my friend's home 8 hours from here, and still had it all frozen solid the next day. I love unpacking the cooler and finding the inside still dry, makes it a lot easier to prepare it for storage (never put up a cooler that's wet inside, unless you like mold).
I've worked this routine out over many years. It sounds difficult, but it's no big deal once you're used to it. I'd like to see how long one of the premium coolers would stay cold following these steps, but I've never found it necessary to own one. Best of all, I'm working right on the edge of free for the price of all of this, and it's really minimal effort.