I have a similar area that floods maybe 2 times a year, but otherwise is very dry. I learned the same lesson you did - wood floats. In 1 small area I experimented with the landscape blocks that stack, but the flood area is alot of clay, and when wet the blocks sunk unevenly into the ground and my nice straight border soon looked awful. So now I have medium-sized boulders lined-up & stacked, with smaller rocks behind to help hold the dirt back to slow the errosion / wash-out. The heavy rocks begin to sink over time, but since it's a more casual look, it doesn't look obvious. Maybe once a year I just lift them & toss dirt or peagravel underneath.
The biggest mistake I made the first year was spreading mulch. It would have been easier to just drop my money down the sewer drain.
In another area along the driveway that flooded about 4 times a year, I dug a 12' trench parallel close to the driveway, laid in a corrugated 6" drain pipe wrapped w/ the long stocking they sell for those pipes, and filled the trench w/ peagravel. When the 'wave' comes rolling off our neighbors property, and across our driveway onto my flower bed, this pipe & trench catches a good amount of water. The water in the pipe doesn't go anywhere, but it acts as a holding tank until the water can slowly seep into the ground below. It's not perfect, but now the area only flooded once this year. I planted a low-growing sedum in the peagravel.

It is my experience that when the river is going over the driveway there is a) nothing you can do to stop the river from going where it will and b) nothing you can do to stop the river from doing whatever it wants with the gravel.

I do have several very large (over 1000 pound) rocks that tend to stay put. Also, I do have one driveway where there is a very long level spot designed to draw the river away from the crossing itself, that is long enough and level enough that the river doesn't move very fast across it.

My two cents