Thanks for the replies! I went to the nursery yesterday to get some supplies for some blueberries I'm planting and they had a 15-gallon Dancy and the fruit was the same ripeness as my tree. I didn't check out the other characteristics, but it looks like you guys are correct! Thanks for the ID!
There's one other mandarin tree that came with the house, and I don't know what it is. When the fruit ripens on it, I'll see if you guys can go 2-for-2.