Do you have room to pull the slope of the dam back to a 1:3 slope and use the dirt to raise the dam? This could be done with a compact excavator.
Ditto that. I had to do some similar work to my dam so I set up with my backhoe as close to the edge as I could get and then reached out to about 2 ft deep water and pulled in from there, gently increasing the slope to about 1:4. Then I backed up a bit and rolled the top edge of the dam. A rolled edge does not allow the water to speed up too much as it drains. Fast water means fast erosion.
After I was done, I turned around and used the loader bucket to back drag and pack the new work from the water's edge over the top of the dam.
