I've heard they don't much care to walk on chicken wire laid on the surface of the ground, because they feel like their feet will get stuck. I'm not sure that actually works, though. I think it's thought to work along the lines of the cattle guards you sometimes see across roads. If you try it, you'll have to make sure the wire never gets covered by anything, such as leaves or loose earth. Another problem would be plants such as grass growing up through the mesh. It would be difficult to lift the wire to remove the grass. That I can attest to from personal experience.
The deer won't be deterred by shiny tape or anything of a similar nature that you put out. Like any other creature, they become accustomed to their surroundings, and once they're used to seeing the tape, it will just become part of the background, so to speak.
Some people have success with human hair, but many others don't. As I said, the deer become used to whatever they see/smell/hear on a routine basis, and it all just becomes a natural part of the environment to them.
Like it or not, fencing of some sort will be your best bet ... or a territorial dog. The latter is more effective than anything else, but if you have close neighbors, you probably couldn't leave the dog out overnight, which is when the deer would be most active. There are commercial products you can buy, but they have to be reapplied frequently.
Some of my friends have been able to keep the deer out of their gardens by planting a "deer garden" on the deer trail. The deer get to it well before they reach the homeowner's plants, and are able to satisfy their appetites. Deer gardens don't require any weeding or much other care. You just plant the seeds or starts and let them grow wild.
"Caging" your pumpkins would be difficult, I think. You would have to cage the entire plant, not just the individual fruits, and pumpkin plants can grow quite large. If you didn't cage the entire plant, the deer would just eat the leaves and stems, and there would be no photosynthesis to support the fruit.
"Isn't it enough to see that a garden is beautiful without having to believe that there are fairies at the bottom of it too?" - Douglas Adams