No, you can't move vining cucurbits. It will kill them. If you have too many, you can remove some. What you can also do is plant seeds of news ones in your additional plot. In your zone, this could be possible.

There is no way your watermelon will end up tasting like cucumbers.

So as long as I keep them watered well and add some fertilizer they should all be fine? I've spread out the rest into well defined rows where I've planted mustard greens and spinach.

I have expanded from the little green patch on the left to this tilled and planted spot. I'm hoping to till and plant pumpkins behind what is currently tilled.

My own belief is that, within reason, yield depends more on square footage than numbers of plants. So each plant will bear fewer fruits and they'll likely be smaller, but the area will produce about the same quantity of fruit.

I can't tell how many plants you have out there. There's a point where all the plants will be stunted if too crowded. If you're worried, best thing would be to cut some of the plants out at the stem. Don't pull them, if the roots are entangled, it'll hurt the plants you're keeping.

And be advised that pumpkins take a LOT more room than melons.

The vegetable forum, btw, has a lot more people who can chime in on this question.