So, I was in the front yard on Saturday, and I saw this for the first time!
It's a volunteer Red-seeded Citron watermelon. The seed it grew from was from a plant that I grew in 2015. The fruits kept better than most winter squash. It volunteered last year, too, but this year's plant is much larger (and this year there's just one plant).
A family member had been watering it, apparently.