It's not so much that they're on the grass that bothers me, it's that I'm worried about running over the vines with the lawnmower when they do make it onto the grass. And then I remembered seeing crops grown at WDW where almost all the produce was hanging down, and I thought hmmm I wonder if that would work. The pics aren't mine, just ones that I found online but... (sorry about the size of them)
You can see that they've actually got quite an eleborate system set up, with a very sturdy framework in place for the vines to grow on and then the fruit hangs down. You can also see they've got clear molds around some of them, so that as they grow they'll be forme into Mickey head shaped pumpkins. For pumpkins that are too heavy to just hang down like that on their own they support them with netting.
So I started wondering what I could do with my little garden to kind of maximize the growing space. It's about 25' x 8' and it has to handle not just the pumpkins but other things like tomatoes, carrots, lettuces, squash etc.