The best that I can tell, this is a sphinx moth larvae. It was quite large and looked a lot like the photos I found of them, but they didn’t quite look like this, so I have assume that it is one of the species, but not quite the ones that I saw on the internet.
It is a moth, though, so that much is true. It was about 4-inches in length and as fat as my little finger, so it was good sized. As late in the year this is, I was surprised to see a caterpillar.