[whaleroad]

I picked one of my butternut squash because they were getting too big and I thought I'd let it ripen off the vine. Never had a problem doing this before. It looked fine and healthy when I picked it a couple of days ago. Then it developed these spots which are quickly spreading.

Assume this is black rot? The fruit on the vines look healthy. So is it best to leave those to ripen on the vine, because I assume they won't store long after picking? One google result suggested I pull everything up and burn, which I obviously don't want to do.

Is the rot more likely to set in after picking?

Note: Like most places, it's been mostly warm and wet here with some cold nights recently.

[New shoot]

That looks like the rot I sometimes get on stored squash over winter if they weather is too mild and warm, or if the skins are not as ripe as they should be.

I’m not an expert on black rot, but I would say it is a mould that was on the surface of the skin and has just taken the opportunity to attack.  The recent mild wet days are perfect for all types of mould and fungi and the nights have not been cold enough to stop them.

Personally I would leave any more fruits you have on the plants to develop thicker and riper skins.  You may end up with bigger squashes than you wanted, but they should keep.