Hi-
I have taken a rolling soft-side cooler as a carry-on to both the Bahamas and St. Thomas. Couldn't do this in Mexico, they confiscate food!
I use dry ice. (check with your airline, most will allow it if you declare it. Plus it is usually gone from the night before by the time I get on the plane.) Food stays really frozen. I found a perfect sized rolling cooler to use as a carry on and the benefit of not checking it is less chance it gets lost. I have read horror stories of getting your lost checked bag back several days or a week later with spoiled food. YUCK, would rather sacrifice one of my carry-ons and check my clothes.