You could send some roots to me...I'd love to have them. Spray Round-up on the rest. Be sure to cut the runners with your shovel first, if you want to keep any, as Round-up is a systemic herbicide that works it's way down from the leaves to the roots. It does not poison the soil, so don't worry about residual effects.
If they are really stubborn, like they sound, kill the plants, remove as many roots as possible, use a weed killer, then till the ground. It sounds good in theory, but I am just guessin' here, pdswife.
Eeek. I just did a search, and those buggers sound bad. Chemicals don't work, and weeding seems to encourage them.
You might try landscape fabric. Another suggestion was to improve the drainage--they like moisture--but if you are in Western Washington, there is a limit to how much you can do to dry out the soil. (I lived up on the Olympic Peninsula--damp doesn't begin to describe the climate.)