I remember reading about curing Winter squash on the North Carolina State University website years ago - advice for commercial growers.
It didn't make a lot of sense. I imagined a truckload piled in a barn. The advice to not leave them in the field until after frost made sense and was put into practice. When the risk of frost becomes too high and I don't have time to harvest, I will cover them with cut corn stalks.
Finally decided to take a 2 or 3 step route to move them to the basement. First, onto a pallet and not touching in the carport. If it may freeze hard enough to freeze in there - into the garage. In there, the squash (and pumpkins) are sitting on a wood floor. Giving them 5-7 days - I think that drying of the cut stems and soil-side skin is important. Final move, basement shelves.
Steve