Reid, if you can spread and weight the plastic only to cover the Artemesia plants, and leave the perennials uncovered, that will work. Don't cover the foliage on anything you don't want killed.
The clear plastic does the same thing as greene's pane of glass, (only it's flexible). Cooks the top growth. Do it on a clear, sunny day, leave it on for a day or two, then remove so you can water the other plants. When the burnt plants start regenerating, put the plastic on for another day. Repeat as necessary. Don't leave it on.
It will be a pain for a few weeks, but worth it and cheaper than a chemical solution, I think.
