THANK YOU Grant Niesner!
It's not a turtle (wtf?), it's not a top-secret diseased mutant from a testing facility, it's not a rodent of any-sort, it's not a badger, it's not latex, and it's not flipping you off.
My inner zoologist died a little with this being such a "mystery". >.<
The real interesting "wtf_nature" going on here is how it decomposed, not its identity. Fish tend to start eating at the nose because it's the softest and most accessible area to get to. The front teeth fell out as is common with decay. When hides are soaked for a long time the hair begins to fall out, thus the "naked" appearance. The colors are from decay as well.
-When seeing heterodont dentition you can guess immediately it's a mammal (there are some exceptions in other animal taxa, but none that look like this).
-Sharp canines such as these indicate the animal is carnivorous or omnivorous. Rodents on the other hand have two large incisors and do not have the lower canines shown in the photos.
-So we have a small to medium-sized mammalian carnivore/omnivore that lives in the long island area. That takes it down to raccoon or dog. Winner is most likely, with that hair type and texture, and foot morphology? Raccoon.