Take a picture from the side Mark. It sure looks like the correct body except the cap notch is very big.
Here is what it should look like from the top on an Fhead with the vacuum advance diaphragm removed.
You should have a Prestolite IAY 4401 originally in a 57' F head. I am not sure what you have. The distributor body is unique to the Continental/Willys L and F 134. Any 134 distributor will fit in the block and index the pump. That is either some form of aftermarket distributor or a modified original for a 134. There are a few distributors used in L and F head motors but for the most part, the body's look the same. The distributor body should be just under 3" in diameter under the cap. Just looking at them the Autolite and Prestolite are hard to tell apart. I think the IAY designation were vacuum advance units but I am not sure. I went through a lot of information when I restored my distributor. It has parts from a few different distributors to make a good one. I do remember reading there are a LOT of distributor versions out there for the 134's. For the most part they will all work.
Ahh it is a 1936 to 1938 Willys L134 Autolite IGS-4007 distributor, with a modified breaker plate and the condenser mounted outside. It also appears as if someone modified it further and installed the vacuum advance or "governor" as it is called in the service manual. That looks like what would have been on the original 1957 distributor but not on the one you have in there now. Some one created the "57" IAY-4401 out of a IGS-4007. Far out man! Here is a shot of a IGS-4007 correctly assembled. You have an old distributor there and way unique.