I have routinely taken a half gallon of ice cream on our Kayak
excursions. It is inside a smaller lunchbox size cooler with about 5
lbs of dryice on top, and that cooler placed inside another cooler.
Works great. The only problem has been that the ice cream was sometimes
still frozen (after 3 days) too rock hard to dispense. It hat to sit
out for thirty minutes to get a scoop in it.

I doubt it's advantageous to use dry ice for a longer cooler duration.
Three days seems to be the maximum. But if you want to keep things
frozen, it's perfect. It's available around here in any local grocery
store, from a special "Dry Ice" freezer by the entrance.