I always thought the rats would bury into the shore, and have their dens above ground. Theyre nesting under the pier, dragging cat tails, etc. What's the best strategy to trap something like this? There's no obvious route in/out, it varies.

I would use floats .

More difficult at this time of the year thanks to WI - no bait or lure out of season law. Body Grips with flagging tape come to mind.

Back in the "olden days" I used to have tires hanging on my dock posts for boat bumpers that the rats would use for feeders. I would get them started by hanging the tire so the bottom inner bead was just above water level maybe an inch or 3 with the tread under the water. Then I would fill it with mud and weeds. The rats would then climb into them and use them for feeders since the tires provided overhead protection. I would place a 1 1/2 inside on top of the weeds and blend it in a bit after wiring it to the dock post. They would hop off then and drown once caught. One fall when the rat population was high and we had a late freeze up I caught 54 rats off of my one dock with 4 tire sets.
If you had a couple of old tires you could try hanging them from the dock and see if the rats use them....worked for me. Floats would be much easier but I am not sure if they would be as effective since they do not work well for me here.

x2

I trap on some big lakes. I find I can screw my stools right to the piles on the down wave side.