Since nutsedge tends to like it moist and sunny, you could exchange the soil from somewhere dry and shady. Maybe the back of the border or under the eaves.

I would not compost the "nuts" or any of the green growth that has seeds even in a hot pile, but in Michigan our options are kind of limited since it is illegal to dispose of year waste in a sanitary landfill, where your regular household trash goes. If you have yard waste pick up double wrap them and put them put for that.
Possibly putting them out, double wrapped in clear plastic baggies, in the sun to be solarized might render the stuff ungrowable.

Kimpa, nutsedge is MUCH more adaptable than you think.

I have it in the lawn and in the beds but I have never seen it in woods behind my house or in my shady beds adjacent to the woods. I just don't throw away soil. How about putting soil with nutlets somewhere and then covering it with cardboard and mulch. Yeah that's what I would do...Or dig a deep hole half way to China and bury it all. But I just couldn't throw away my soil!

I put that kind of unwanted garden waste deep in the woods where it doesn't grow. If it's diseased, it goes in the trash can.

Thanks for all the ideas. I'll need to give this some thought...just scared to put this somewhere else in the ground.... Have an area with very poor, dry, but sunny soil... Maybe a deep hole there...
Beth