On my search, I noticed that it is a tab rooted tree. As I remember the recommendation is to cut it as close to the ground as possible, and apply herbicide with a paint brush just to the cambiam ring--the area just inside the bark. This is minimal use of herbicide (glyphosate) but I understand your reluctance to use it especially in a pond area.
Some people cover a short stump with a food can if you can find a big enough diameter one.
I would try to damage the cambiam as much as possible, because that is where the energy comes for the plant to send up a new shoot.
