Eric I struggle with squash and pumpkins too. For pretty much the same reasons. And can grow summer squash that fruit as large as my thigh.
That's usually true, but not always, and when it isn't true I think there are a couple of complicating factors like location, plant genetics, pest-predator cycles, luck, etc.
Butternut and acorn have been vigorous and productive and still eventually succumb to the yellowing, mushy vine. Usually late enough in the season I consider it a win, and sometimes can even blame the cold.
The huge but is that I'm not sure the yellowing, mushy vine is caused by those grey squash bugs. Their population is easy enough to control. You can find their eggs before they hatch. Luckily those eggs are easy to spot. Coppery colored with a metallic sheen that pop when squished. Almost always located on the underside of leaves in a cruck of the veins, rarely on the vine stem too.
I'm told it's also possible to control population with later planting dates--after they emerge in the spring. A local market melon grower uses later planting dates to stymie these. (He plants later--up until the 2nd week of July-mostly to hamper his bane, cucumber beetles. Muskmelons are significantly more vulnerable than squashes.)
They're sap suckers those squash bugs, not vine borers.
There is such a thing as a squash vine borer. Melittia cucurbitae is the scientific name. I think they're the yellowing, mushy vine culprits. I can't speak to population control but there are a couple cultural practices that may help.
Squash can
root from the leaf nodes on vines. Cover those nodes with inoculated chips/dirt as the plant expands. Honestly I never think the
roots get large enough to support a single squash, but it probably helps? I can't say this is definitively the reason I get squash, I can't disqualify it either.
Another suggestion is to use aluminium foil (or another physical barrier) to cover the main stem where it meets the soil. Can't speak to this effective as I haven't tried it. I would do it as I transplant, cover a couple inches of above ground vine and an inch of two of vine below the soil.
The white powdery stuff on the leaves is likely powdery mildew. I do use milk to knock it back, like 1 part milk to 9 parts water. The milk mixture is really effective to limit it's spread, especially if you catch it early. Spray every part of the plant you can. It might work as a preventative, I have never been that on top of my squash game though.