Spray with CrossBow -- but cover the plants you want to keep. This is a very potent control; even so, expect to have to follow up again with another round of spray. That vine is the devil incarnate!

that would work if that %#*!$*!! were in the open on its own, but it's twined around the bananas and ti plants and creeping through the impatiens, and all the roots are mixed up together.

We found out we got it from a load of horse manure. Got spread all over the property...

The only way I've ever managed to successfully and completely remove Maile Pilau from an area is to painstakingly pull all the roots out by hand. You can't yank on them impatiently or it'll just snap off above or right at the roots. No, its not convenient, but yes, it it thorough and it works. I never use poisons or synthetics in my garden, so my methods are a bit different.

Got rid of it all...sold my house.