Do you know what variety of pumpkins you are
growing? Some take more space than others, some hybrids were bred with a compact vine in mind, but keep in mind compact still eats up some good sq footage. I'd say generally plan to get 3-5 usable(fully orange at harvest) pumpkins per vine. It can vary a lot I've found due to weather, bee pollination, and soil conditions. I'm not sure what you meant by 4'x4' in 6 spaces, I'd say 10'x10' per vine in my experience for the jack o lantern and more for bigger varieties 20'x20' minimum. Do you have corn or other areas like lawn you don't care to mow that you could let the vines ramble through? You can move the ends of vines before they send out roots to help direct them place & trim vines, but they usually don't
flower any closer than 8' from the main root. Trimming the lengths will reduce yields also.
Can't help with watermelons the just don't do good for me, the biggest ones I've ever got were the size of softballs!
Pumpkins on the other hand do great and I love
growing them!