Definitely let them take root further up the vine. At the nodes where the leaves/flowers come out, you will also notice additional roots start to develop. I like to bury my pumpkin vines, for 2 reasons, so that they take root, and you get better root systems. And also to lessen damage to the vine from pest such as Squash Vine borers. The vine could survive damage from them if they are rooted down in various places vs just one place.

Thanks ccabal! I just hate to dig up the whole area... I may just try this: as they grow, choose some sections of the vines to "bury" by moving aside some mulch, slit the weed barrier, put those leaf nodes in contact with the soil, and recover with mulch. Hopefully that will help the root system, and deter at least some of the borers?

Thanks weirdtrev! "Less work" is my middle name :)

You ask does each pumpkin plant get all its needed nutrients water and growth from the root zone only in the mound well that is a double edge sword question yes it will but then you are limited on plant growth and fruit production and will have to more severely prune back you pumpkin about 1/3 habitually periodically all season so my advise and I have done it as well as others is once in awhile along the vine growth bury a section of the vine between the leaves all you need to do is slice a hole in your mulch cloth to do so and it will set new roots and tremendously eventually root and feed the plant much better! Do this before it gets to late in the season but be careful and be sure to still trim back excessive long tip plant growth so the rest of your plant can put its energy toward developing more and bigger&healthier pumpkins that will harvest before its to late to much growth to a certain point slows down not only the size of the pumpkin but it slows down the ripening process aswell as limits the nutrients going to the fruit so use the 1/3 off the plant rule of thumb when it gets to be a fairly good size and maintain it at that and you will notice better fruit and more side shoots in a smaller area of harvest

Connecticut Field and Spookie are both of the Pepo species. As I understand it, and I could be wrong, is that Pepos do not put down adventitious roots at the leaf nodes. None of my Delicatas nor any of my summer squashes do it. Nor have the three Moschata varieties I have grown. But all of the Maximas I have grown have developed adventitious roots, including Prizewinner Hybrid Pumpkin. Can anyone answer definitively about species vs adventitious roots? Is this just a trend I've observed or is it a dependable rule?
Even in the absence of adventitious roots, the roots from the main stem likely travel far and wide as do the runners above ground, so it still makes sense to have moist, fertile soil for quite a distance away from the main stem. In my experience, this is what makes for a truly prolific squash plant.

Some Pepos do... I've grown sugar pie pumpkins, and they definitely put down roots at every node. Acorn squash don't seem to put down as much. Yellow crookneck doesn't much either.

My Spookies and Connecticut Field pumpkins are both sprouting roots at the leaf nodes. See photo.

Follow-up. Here they are, just over 6 weeks since planting the seeds. Photo shows two mounds of Spookies. We've had a solid month of hot humid days, followed by rainy afternoons (almost everyday). Getting lots of flowers and setting fruit this past week. I'm trying to bury the vines - at least somewhat - in the mulch. I'm finding that the young vines and small flower buds are prone to damage if I mess with them too early... but when the vine gets more mature, it gets stiffer and harder to work with. I've also taken gfjbthllr's advice and pruned them back some this week. Doing what I can.

One of my first Spookie fruit... also at 6 1/2 weeks since planting seed.

Those look like roots to me. I guess I was right when I said that I could be wrong.

Same fruit today... just under 8 wks since planting.

Final follow-up: that pumpkin I photographed above about a month ago turned orange and never got much bigger than that. All of my plants have suffered an endless onslaught of squash vine borers, squash bugs, cucumber worms, powdery mildew, and other diseases. Seriously, almost every common "plague" I've read about in this forum, I've been hit by. I tried pesticides, fungicides, hand-picking squash bug eggs off of plants,... you name it... but I just couldn't slow the damage. Last week, with 90% of my vines dead or dying, I pulled them up, and harvested about a dozen 7" pumpkins - some of them orange... some orange/green. After all the chemicals that have been spread on them, I don't dare eat them. If they keep 'til the fall, they'll make cute little jack-o-lanterns. I don't think I'll try pumpkins again. :)