Re: Ripening Winter Squash
I've never bothered about the bit it sat on and I've kept them until the following October in edible condition.
My suspicion is that the sun bathing bit is more about raising the sugar level than hardening the skin on an already ripe squash.
Not quite ripe ones should just be used first.
Do leave them on the plant until the leaves die back, then remove them pronto to avoid bipedal pests.