The only thing I can think of is trellises and letting the vines run out in the surrounding area.
I am glad that I found a kindred soul who also can't get herself to kill perfectly good plants.

A-frames, especially if about 6' tall. Large pumpkins can be supported in a hammock made of an old T-shirt with the shirt ends fastened to a crossbeam; small pumpkins do fine in a hammock made from old pantyhose; tiny pumpkins don't need support. Check out yard sales for *cheap* stepladders; they make excellent A-frames and can be folded to put away at the end of the season. Wind the vines up and over the frame, exceptionally long vines may need to be spiralled around the frame (6-foot ladder gives you 6'+6' of vertical space, one spiral around provides about another 4 to 6'). The area under the A-frame does nicely for a shade bed for lettuces, etc. Don't forget to surround the baby pumpkin plants with radishes to deter squash borers.

Thanks for the good ideas. This is the first summer plantings I've done in the 4x3 box, so everything is an experiment.
anneliese, I had not thought about the trellis idea. I have a couple of small ones sitting around, so I think I'll go with that this summer.
meldy, I like your idea of an a-frame trellis. I found some sites on the web that explained how to make them and I sent the sites to DH as a "hint" for future trellies.

Good grief and sigh "squash borers". Ok, I'll plant some radishes.

DH got a great idea. He will make an A-Frame trellis out of our old metal trellises. Thanks for your suggestions.