When my squash plants have had the most dramatic problem with squash bugs is when the plants have been stressed from lack of water. It was easy to see the problem a few years ago. A sprinkler failed so that some plants in a row received an adequate amount and were doing fine. Where the failed sprinkler wasn't doing its job, the bug situation was dire.
Perhaps, the tendency of mulch to not only protect soil moisture from evaporating (a good thing) but to soak up water before it reaches the soil surface (not so good) is sometimes part of the problem. Then, the pests also scramble around and hide.
Without mulch, they just hide under the leaves and stems in my squash patch. Pyrethrum inhaled knocks out insects - it's a nerve toxin. Not persistent and I have read that if the dose isn't fatal, the bug may be actively back to feeding on plants in a few hours. Pyrethrum may find them where they hide but I don't know if that includes heavy mulch.
Interested in how
Tromboncino summer squash and related
Cucurbita moschata winter varieties do in other gardeners' experience.
Steve