Hey conpewter,
I remember the discussion on Tordon. The thing is that it's not necessarily easily obtained, and I do have some concern that it might be overkill and about any resulting collateral damage. Also, as strong as it is, I wonder if it might kill the vine before the poison did an adequate job on the roots. Roundup is also a systemic poison, but is a little more user/environment friendly. Roundup also has a stronger poision for woody plants, from poison ivy to tree stumps, but again, overkill/collateral damage as it's not recommended for use in gardens or in close proximity to desireable plants.
I've actually read of people having good results using Roundup on bindweed. Sure, you could spray individual vines, but that seems to have pretty limited success, and takes a while to do the job. I've also read of people cutting the individual shoots and applying the poison with a q-tip, but with the way this stuff has spread I'd have to take the next few months off of work to do that. The most effective application seems to be to strategically select vines of the plant, ball them up and put them in some sort of containter with a slightly dilute solution of Roundup. Obviously you want to set up the container so it can't inadvertently spill or what have you. The reasoning behind using a dilute mix is to make sure the plant gets a good drink of the stuff so it gets well into the roots before the vines die. The fellow who came up with this particular method (others have suggested putting the vines in a plastic bag and spraying them down) said that, before long, even vines across the street started dying. He let it go for a number of days until the vine was black and most certainly dead. Then he'd move to another spot and repeat the process. Beyond that, individual sprouts can be pulled or sprayed as they come up.
I'm planning on going at it this weekend, after I get my trellis up of course.