Welcome Mark !
My first guess was some kind of wild morning glory, then when I read Allison's Wikipedia reference it mentions the morning glory family. We have an area in our gardens that was built up a few years ago from fill brought in by a contractor. It wasn't the cleanest fill in the world, but it was cheap. I then put a layer of clean top soil on top of the fill. Ever since I have been battling a similar vine that does the same thing as the ones you have. It winds it's way around anything I plant in that area. It grows very fast and looks just like a wild morning glory. About every two to three days I go through that area and pull any of them I see. I don't snip them as your landscaper friend says. The vines grow from "mother roots" that are under the soil and can be quite extensive. Pulling the vines I see separates them from the mother root rather than just severing them at the ground where they can easily grow again. It's been a battle, but after a few years, I think I am winning. I am not seeing as many anymore. My theory is by diligently eliminating any vines that start to grow, I may be depriving the mother roots from nourishment, and they may be starting to die off. At least I am hopeful. Look closely, and you will see where they are coming out of the ground. Pull easily, and if they are similar to the ones I have, you can often pull them from the mother root rather than just breaking them off allowing the same ones to grow back. You'll know you severed one from the mother root if you get a piece about 4 to 6 inches below ground to come along with it. This piece will be a much lighter, almost white color, and will have no roots. Forget about digging the whole area up and trying to remove the mother roots. If you miss even a small piece, the plant will continue to grow sending up new shoots. The more shoots, the more the mother roots are being nourished, so you have to be very diligent in staying after they new ones that emerge. Hope this helps.