RUMBLON,
When we purchased our farm, we had invasive Honey Locust trees, Siberian Elms, and cedars.
The cedars are the only woody species on my farm that dies when you cut it off below the lowest branch. EVERYTHING else requires chemical treatment.
I can get the elms with the recommended Remedy/diesel mixture. To kill the locusts I have to use weapons-grade systemic herbicide that is deadly to fish in very low doses.
My advice is to look up the appropriate service department in your county in Idaho. (It is called the Noxious Weed Dept. in my Kansas county.)
If you find the right people, they should be able to tell you the exact procedure to most easily and safely kill off the willows on your dam. They also sell me the chemical at cost, which is significantly cheaper than internet/big box store prices.
I suspect you would like to avoid using chemical intervention. However, most of the willow species can be planted just by taking a cutting from the branch of a mature tree. I seriously doubt you could grub them out effectively.
Describe your exact conditions to the county expert, including your fish and waterfowl that need to be protected. They should be able to give you a good recommendation.
Good luck on your pond project! Hopefully, you can even get an expert from Pond Boss that has won a battle with willows.
