I don't know enough to say all, but I think most climbers would do fine draping down. My father planted strawberries and ivy on the roof of his garden shed which definitely got the idea and grew over the walls like he wanted. I have also seen neighbors with grapes in hanging baskets, which sent me looking for the other plants you mentioned in hanging baskets online, and I found plenty of examples of each. I also learned that it can help your cucumbers grow straighter!
image from Food Gardening Network
As to other edibles to try this with, I can't really think of any not to try it with. Please write an answer here with your results if you do try it! So long as they are supported enough that the plant doesn't physically break I think most plants can grow in some pretty wild orientations.