It's not quite slash and burn, but it might be closer to "Nuke it from orbit, it's the only way to be sure."
A year and a half ago, my wife and I bought a home. It has a garden plot about 75x75 feet, then cut diagonal (triangle shaped). It was terribly overgrown with 'crap', for lack of a better term. Everything was head height or better. I cut it all down to ground level, even the raspberry bushes that we discovered (they'll grow back, I know). Then, I pulled every plant out that I could find and burned it. There was still a weed or two, so I did what any sensible person would do....
I tilled it under come spring!
Then I decided to actually look up what the most prolific, and only surviving weed, was.
That was how I discovered how 'awesome' bindweed is. All last summer, I diligently pulled it at all possible opportunities. One person and that garden, while working full time, is no match for bindweed that's been tilled. The potatoes are the only plant that fared well with the bindweed. I religiously hacked away all bindweed that thought about getting near those particular plants, even if I couldn't get to the rest.
This year, I'm taking a different approach. I got RoundUp concentrate with the pre-emergent and figuratively nuked the entire garden. All of it. Then did it again a few days later because I still saw green. Then I left it. It's now two weeks later and I have the entire garden covered 100% with 4 mil black plastic, weighted down with various large rocks to avoid tearing like stakes would do.
Is this a guaranteed cure for bindweed? Should I have used another method? I'd heard bindweed can grow enormous roots, but until today and reading GW, I thought they'd only go 1-2 feet underground. Obviously I was wrong...
What else should I be doing to kill this crap?
Another quick (and slightly humorous) story. I found tons of weeds with a round, waxy leaf growing in my grass. I diligently pulled it up, root and all, and tossed them all into a pile, whereupon I hit it with the lawn mower so I could suck them all up into the cuttings bag.
That waxy weed was/is purslane. After I did all that, I looked it up and discovered that I wasn't seeing the THOUSANDS of seeds that each and every plant has that I had now dumped everywhere on my law.
I'll be fighting these with a simple pre-emergent this year and re-seed with grass next year with the bare spots. Any better suggestion? I have time.