Ric, I don't want to even try to speak for Kelly but will give my experience with willows.
I use Remedy, mixed with water, as a foliar spray. I sometimes have to respray . I assume that I missed an area. It is deadly. I don't use diesel on the trunk area because of the cost. Remedy, like most herbicides is darned expensive. When mixed with diesel, as a trunk spray, the recommended dosage is four to one. Sure, it doesn't take as much per tree, but when mixed with water, it is mixed around 80 to 1. A 10 to 15 gallon load, in my sprayer for the 4 wheeler, goes a long way and lets me divert to poison ivy, oak trees and brush, green briars, etc. The 10 to 15 gallon load takes about 1/2 cup of chemical. Thats not too bad at about $100 per gallon. I've tried dishwater detergent as a surfactant and also the stuff (don't remember the name) that Kelly recommends. I feel like the good stuff works best but usually run out of it and go back to liquid dish soap.
Dang, I'm glad I don't have beavers in my pond. The coyotes and bobcats took care of them at the creek.