John,
I do know my way around beaver dams. I have removed hundreds of them, some of them monstrously big.
The key too it is to get some water coming through it and let the water flow do most of the work instead of lifting the mud and sticks with your weak back.
This particular dam was only 6-8 inches of gravel. I looked at it and figured that this will be quick work. Wrong. Gravel is heavy and there was not enough water flow to help.
Its been 3 days since I jacked up my back. I can stand upright without screaming today, so that's a good sign.
I'm going to see the doc tomorrow sometime.