Advice on clearing out a bed

[aninocentangel]

I have a bed on the SW side of my house that is bursting with a male trumpet vine, the kind that you order cheap from those shady catalogs that sell tomato trees that produce ten pound tomatoes. Yeah, that's the one.
The bed also has some holly and an azalea, which I had been trying to save, but at this point I'm ready to give up on them and just get the thing cleared out.

I've tried putting boiling water on it. That killed the the plants where I poured the water, but they just zoomed up through the rest of the bed that much faster. Last year I declared war and dug everything out of it, hitched a rope up to my car and pulled the big clump of root out and then sifted through the soil to get as many of the roots as I could. I was armpit deep in the hole still pulling out roots nearly as thick as my wrist when I gave up on that. I washed all the dirt off the shrubs, meticulously picked all of the trumpet vine out of their roots, and put them back in. The trumpet vine was back within a week. (side note, I though the root grooming would kill the holly and azalea, but they're doing better than ever this year too. I also discovered that I'm allergic to holly.)

This year I just want the stuff gone. It's tearing up the house. Last night my son showed me where it's grown under the siding, through his window screen, around his storm, and into his room through the weather stripping next to the window lock.

How the heck do I get rid of this stuff? At this point I'm open to all suggestions, including herbicides, petro-chemicals, heck I'd almost try nuclear waste but I'm afraid that it'd like it.

Thanks for your time.
Enjay

PS the trumpet vine was something inherited from the previous owner, he planted it the spring before we bought the house. Had I known then what it was I'd have torn it out immediately, but they promised me that it would produce big yellow flowers that attracted hummingbirds, and that it would just grow on the pillar right where it was planted. It did, as long as I took the machete to it a few times a week.