How to control a vine?

I have some distictis "Rivers" growing alongside my porch. I'm glad that I have finally found a vine that does well in adobe soil, but not so happy about all the shoots (suckers? whatever you call them) that are growing through the railing and across the porch. It's getting to be quite a chore to keep hacking them back.
I did some online research and called some local garden stores but haven't gotten a definitive answer about whether there's something I can put on the cut places to keep them from growing back. I wrote to both Monterey Lawn and Garden Products and Bonide last week asking about their Sucker Stopper and Pruning Sealer products, respectively. The information on the cans and the websites talks about healing cut areas, but nothing about preventing regrowth. Oh, and the information only mentioned trees and woody ornamental plants, not vines.
I got a note back from Monterey saying that it should work. I haven't heard back from Bonide.
So...does anyone here have a recommendation for something I can "paint" on the cut areas to stop them from regrowing without hurting the overall plant?
BTW, there's a product on Bonide's website that some of you may want to stock up on for tonight. :-)
http://www.bonideproducts.com/products/product.php?category_id 0
Unfortunately, the link to the label isn't working, and the MSDS is not very forthcoming (it implies that the product contains water and chamomile). Nor is there any availability information, so you might have trouble finding it in time...
Patty
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