vine control (oh lord help me) Phx zone 10

So we have these AMAZING squash -Tohono O' Odham squash. We call them The Hideously Prolific. The white and green fruits are bigger than pumpkins - huge delicious yellow-meated squash, which produce lots of fat two-inch seeds. It grows great in full sun on 100+ degree days all summer long. The meat is delicious and the seeds are great fried in oil and salted.
Problem is, the plant is aggressive like whoa. Think Genghis Khan. It has gorgeous green and white fuzzy eighteen -inch leaves (I kid you not). The tendrils are over a foot long (there are four tendrils on each leafing branch), the flowers are bigger than my hand spread out, and last year the vines climbed over our driveway, our roof, our sidewalk, and climbed our two-story mulberry tree. The vines are furry and thick, completely impervious to insects. You'd have to see it - we bring friends over to see it and they just stand and stare for a minute. It's kinda scary - but fun.
I have three of these monsters planted this year, and they're taking off. What I'm wondering is:is there a way to pinch back the extra vines to encourage just the fruiting branches? How can I tell which baby vines will bear fruit and which won't is there some pattern, like a Fibbonaci sequence, that can tell me which sub-vines to develop and which to pinch?
Each leaf has a tendril, a leaf, a flower, and a baby vine. So the plants just grow like mad and each leafy branch produces more and more vines. Since the vines and leaves are so freakin' huge, I'd like to find a way to predict which sub-vines will produce fruit and which won't. I don't want to lose a single female flower, but It doesn't make sense to provide space and water to a bunch of crazy vines, when there are so many more male than female flowers.
So far I'm letting every sub-vine develop until it produces a female flower, then I pinch it off. But with every leaf producing more vines, and every vine threatening to eat someone I love, it's getting out of control. It's already reached the roof , the gazebo, the pond, and the mulberry tree. Last year my husband had to climb the tree to gather the squash before they fell on someone. We were giving massive squash to everyone we knew, and we ate it all year.
I have seeds for those of you brave enough to try this monster for yourselves - but it's probably best for you Southwest people. This guy loves really hot bright days.
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Tenacity,
I just ordered some of those babies from Native Seed Search. I've become fascinated by native seed strains of garden plants generally, and especially by those grown by the Tohono O' Odham. It's exciting to hear what's in store.
Vernon
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