Not sure on the laws in your state, so some advice may need to be adjusted to be legal. But I often may set traps on a drowner that are actually out of the water, and cover them lightly with leaves or whatever to blend them. They will work just fine set on dry land, and as the water rises it will raise over those traps and cover them so they become a conventional beaver set. Just make sure you put your bank stake far enough up the bank so if/when the water rises you can still reach it to pull your trap. I've dealt with a lot of rising and falling water like you describe, and even did a small amount of trapping in tidal water, where you were dealing with predictable 6-10' fluctuations every day. Bottom line is it is a pain, but you just set your traps where they will be working as much of the time as possible. If there is too much water over them, the beaver will just swim over them. But if it just rises a limited amount, a trap set for a front becomes a back foot set, and one set on dry ground becomes a water covered front foot set, etc. Just try and picture what it will look like when the water rises, will this still be the logical approach for a beaver when the water is a foot higher? two foot higher?
Conibears in certain situations can be very nice in fluctuating waters, but some places they must be submerged to be legal, and if water falls this can be an issue, also, high water often brings debris with it, and a lot of debris that may simply float over a foothold will catch in a conibear and plug it up.