I am at my absolute wits end.

We bought my mother's house 2 years ago. She was a gardener but back problems kept her from tending her garden for about 5 years so it basically went wild. There are some perennials still growing but the yard is gradually being swallowed by gooseneck loosestrife. I have tried literally everything to get rid of this. Roundup, mowing, boiling water, hand pulling, smothering, etc. The back yard is approximately 1/3 acre and the loosestrife is covering about 75% at this point.

I know that it spreads by runners underground which is probably why my efforts have been pretty much in vain.

County extention had no help to offer other than what I've already done, since this is not considered a noxious weed in my area. (It is basically an escaped ornamental.)

I am willing to sacrifice the good plants to start over without loosestrife. My question is, will a controlled burn kill underground runners or damage the plant to the point runners will eventually die?