I'm told it's hopeless, but maybe some genius here has a solution.

I had a pair of Hibiscus vines taken out several months ago,
supposedly the whole root.

Hah, and yet again, hah! It's coming up all over the place. I am
willing to do almost anything to get rid of the root system. The area
involved is not near anything else that would be harmed. Gardener
says not even Roundup will do the trick.

Is there ANY way to get rid of it?

TIA