Permie Solution for Dog Fennel?

We're trying to reclaim a section of poor, overgrazed pasture. The dog fennel (Eupatorium capillifolium) is taking over the world! For one brief second, the Roundup looked pretty good ... no, I'm not actually going to do that, but I'm getting desperate. Any ideas?

Did you find a solution? I've let a couple stands get established on the septic field and i am wondering if i need to do them in. And if n need to do them in, the only think i can assume is going through a great deal of chop and drop (elsewhere, since don't want to build up mulch on the septic field) for a ...season? ... few years?