Burning just makes smoke. Big flash and nothing accomplished. I have some pretty good case studies, one thorough one from Ohio State University. Cattails are close to indestructable. You either excavate them completely or kill them from the inside. And heavy spraying on that amount is going to be costly and potentially an environmental nightmare.
I would most assuredly go mechanical. There are a few industrial type cutters out there. A simple brush cutter may be a life long labor. But your best bet is my 3 S method. Submerge, cut them off below the surface, which Suffocates them by cutting off all air, and eventually Starves them. This works with almost any rhizome submerged plant. Other benefit is no seed heads or catkins ever form. It may take a few cuts, but on 1 or 2 acres worth, you don't have a lot of options. Also, in my area the number one method of spread by far is rhizome. I have a few areas started by seed, isolated, but almost all new growth is expansion from established growth. I have dozens of photos, and know the biology of this plant inside and out. You have to eradicate the rhizome.
