I'm afraid that my yard is overrun with the things. They are quite
prehistoric, and I actually have a shale fossil of a plant that is very
similar.

I've been pulling them for a year, but if I leave the tiniest bit of root,
they just grow back.

I've tried paraquat, glyphosphate, and 2-4-d. They seem to enjoy it.

I don't want to use a soil sterilizer, but I'm stumped.

Thank you in advance