Anyone ever tried (and succeeded) in getting a Trumpet Vine under control?

[Siwsan]

There is one in my back lot that I've been battling every Spring. It's taken over my garden fence (which, to be honest, might be all that's holding that section together) and springing up EVERYWHERE.

I've read that boiling water can kill some of the vine but that's just not a viable option. I've been using snipping off and using Brush Kill on the new growth and have cut back some massive vines.

Any suggestions, short of torching it? The flowers are beautiful and attract Humming Birds so I'd like to keep a tamed version.