Block ice does last longer, but does a crappy job cooling. Dry ice does a crappy job if it's underneath everything, and if it's on top, it freezes everything. Good for transporting frozen stuff, but not a good choice for living out of a cooler.
Can't say I've ever done a month, but have done a week multiple times. Here's what I've found.
1. A good cooler is a must. Stay far away from 1 day coolers. One that advertises 3 or 5 days or whatever is fine, and you can get those for reasonable cost. If you wanna go all out get a Yeti or something along those lines, but they're pricy.
2. Cooler MUST have a drain. No exceptions. Nomatter how good of a cooler.
3. Drinks on bottom, placed upright, and enough of them so that food could sit on top of them if there were no ice. Then loose ice, then food on top.
4. Every evening and morning, drain the cooler of it's water. Add new ice as needed.
The food's on top so it doesn't get wet, and even if so much ice melts, it ends up resting on top of the drinks, above the water line. Just gotta keep the water line lower than the height of the drinks. By draining. Which is easy to do with a drain, you don't gotta remove everything to do it.
On my cooler, in the hotter months typically I lose about half my ice in a 24 hr period, regardless of how much I started with. i.e. I could make it 2 days if I had to. But usually I replenish once per day so that I'm not always worried about it. I'm sure a better cooler would extend this time. A larger one would probably allow more ice to start and extend it as well, but also require more drinks to keep the food high. You could also do a combo of block ice and loose ice, and probably make the loose ice last longer.
If you don't want too many drinks, a tall skinny cooler is better because it takes less drinks to cover the bottom. It also takes less room in the car and tends to be a better height to make a makeshift seat. Gotta drain more often though because it gets deep quicker.
Tip: As a separation between ice and food, the ice bag works well.
