Thanks for participating on our site and asking questions. It's participation from people like you that make it all grow, and make it worthwhile to me and my partners.
Finding snook - like finding any fish - depends on finding the structure they populate. If you're walking the beach looking for shells, to your side is that Gulf of Mexico, and what appears to be either a rough or smooth surface, depending on the wind. You've said that you fish the "Fan" to keep your baits along the beach and in the trough, which is definitely the right place to start. Most of the big fish are, in fact, closer to the shore itself than most anglers - especially the ones fishing the surf - would think.
That said, you will improve the chances of getting a strike if you try to locate small structures - even within the context of the beach. I do not know exactly where you're fishing, but look for small rock outstructures. Look for small 'pockets' of inset area, perhaps where rain run-off caused a little erosion. There is structure there, even if it looks like a long stretch of straight beach. The line is not constant. Another thing to look for are "eddies" in the water. Flows that seem to show two different 'mini-currents'. Little "S" shapes, little "V" shapes, and even little spaces where the water seems to be moving but really isn't. And lastly, I suggest you read an article we put here recently that talks about something called "The Three P's". They stand for Points, Pockets, and Passes". These three common structural entities do not have to be 500 yards wide, or 200 feet around. They can be tiny. A pocket or point or tiny pass on a long beach could be three rocks that form a little eddie on one side or another because of the tide.
Lastly, try live bait. Get yourself a little yellow vented bucket to hold live shrimp. Buy them just before you get onto the sand, and get the bucket (on a long string) into the water in front of you to keep the shrimp alive. Try using a fishfinder rig to put that live shrimp into that trough reached by fishing the "fan" method. If you can't get live shrimp, cut strips of squid to make long "tails" that wave beautifully in the water. Bait is always the best, and using artificials, while exciting and fun and challenging, reduce the odds you'll hook, fight, land and release that 42" snook that's waiting out there for you. If you do use bait, try a white bucktail jig. Make it a little heavier than you think it should be (but not much) and bounce it like you mean it from the bottom. They will usually stir up life even where none seems to exist.
We hope this helps. And thanks again for being part of our family.