How about trumpet vine? Mine is very well established (was here before I bought the house) and has gone clear under the driveway to a garden on the other side. It goes into the lawn, but there it's mowed down weekly so isn't a problem.
I didn't know some of these things - like cutting it down in the spring (already too late for that this year, but maybe I'll do it anyway). I've tried Roundup on the shoots in the other garden without success. I'll give boiling water a try there.