Well, you could try this...

I had unfrozen gel ice packs confiscated by TSA from my soft carry-on cooler one time. They weren't frozen because they were to be used on the return trip. It never occurred to me that the gel was technically a liquid.

My solution for the trip when I needed something in the cooler? Bags of frozen peas. If I were you, I'd get something like that and put them in a strong freezer-type Zip Lock bag to sit on.