This year we've started eating nearly all our fish as sashimi. I can tell you, with 100% confidence, I know right away if I have left them too long at this point. It may not matter cooked, but eating it raw, it needs to be handled properly, or it comes out rather gross and it IS noticeable.
This year, anything left over an hour after killing it without ice, went straight into a freezer bag labelled smoker fish. This was even up until a week ago, on a rainy day at around 10C, and the fish were kept in the water. Even if the fish were identical looking, I could tell which one I killed first and let sit, and also which side was down in the water, and which was out of the water. If it gets too warm, the meat will start separating, even if the fish is a bullet and otherwise has "firm" meat.
I now have a cooler in the back of the truck, and if I'm close enough, I'll quickly clean the fish and run up to the truck to throw it in the cooler. I always buy those Costco water bottle packs, and once I'm done drinking the bottles, I'll fill em 3/4 full of water and turn them into ice packs. One bottle on the inside of the fish's cavity, and a few bottles surrounding the fish, made a considerable difference in the meat as far as I could tell.