I'll try some of each if you're digging anyhow.

Good question jxa44, and good answer by gardengal. Just like in real estate, invasive potential is critical to location, location, location. Nassella tenuissima is not about to be pulled from the market. It is, however, not suitable in ALL locations. It's a very useful grass for certain areas, but with all grasses and plants that re-seed, some locations are not wise for planting. It seems that the term 'invasive' gets thrown around about as much as 'native'. Both are relative to location. Nassella tenuissima is actually a native grass in TX. Of course, seeking plants simply listed as 'native' is not always the answer. Everything is native to someplace, but that place may not be where you live. AND...non-native does not define a plant as invasive either. There are some interesting and surprising plants listed as invasive in some part or other in the US. These include, among others, nandina, euyonymous, butterfly bush, parsley, daylilies, black-eyed Susans and even Japanese maples. Unfortunately, since you didn't list where you're located, it's impossible to answer any question about a plants potential in YOUR area.

This grass goes into dormancy during the heat of summer, and does not grow during that time. The fact you can pull up clumps indicates at least part of the crown has died, but it's difficult to say why. I've been growing it from seed for several years now, and seldom have had a plant live beyond 2 years. Its re-seeding and short life have gotten the better of me, and I'll be digging up my last three plants this winter.

Thanks all. Jungle87, I have a better idea, why don't you come pull them and take all you want? Actually I've pulled most of the larger weeds, removed the top 1/2 to inch of soil (with the hope of removing more of the dratted feather grass seeds) and will now lay down landscape cloth (easier to get in quantity than newspaper - although I would prefer newspaper because it breaks down and adds something to the soil) and then lay 3-4 inches of shredded hemlock bark on top. That, I hope, will do the trick. Cheers!