Haven't used a cooler with the TT, but then we've only been out once since we bought it in March. We do use Coleman 5-day coolers on the sailboat. If we're out for more than a couple days I'll freeze water in a gallon jug or get a block so it stays frozen a couple days.
If we're going to be out for a week then we'll have 2 coolers and add dry ice to the mix. First cooler (generally the bigger of the two) gets loaded with pre-packed, frozen meals in gallon ziplocks. Then I add some jugs of frozen water and dry ice on top. Sometimes I'll throw in regular ice too, but I think that speeds up the dry ice melting. That cooler only gets opened long enough to pull out dinner to thaw.
Second cooler, which doubles as the step into the cabin, acts as the fridge, except for some frozen water bottles and maybe some dry ice on one end. I use a piece of cardboard to separate the frozen from the non-frozen in that one. It gets opened a lot more than the other one, since it's got drinks, etc.
The dry ice doesn't stop us needing to buy wet ice at some point, but it does let us push the first ice run out to the 3rd or 4th day.
I've also been known to wrap the "freezer" cooler in a space blanket or some of that silver coated bubble wrap. That helps keep things frozen even longer, though it's a bit of a pain to wrap & unwrap. Can't do that with the "step" as it's a very tight fit as it is.