Roundup everywhere when the soil begins to warm up, then spend an hour per square yard, and dig it all over a spit deep!
It's a brutal point, and sadly no help if you're stuck with the problem, but really, this is the only way to clear the wretched stuff properly - and for good (or nearly)!
The additional issue with couch, is that it will certainly regrow where you want your rasps etc., and that means more work to move everything every few years.
As it's an additional plot, just take it yard by yard, and even try to dig (without Roundup) through the winter, if we ever get a dry day, because it'll save you so much time in the new year.
When you get your result, you'll have beaten the damned stuff at its own game!