I had a cousin who was a career air traffic controller in the Navy who had a similar Hammy, could be the same one, but I can't be sure. When I asked him about the big crown, he told me that the guy he bought it from told him it was so the crown was easy to use while wearing gloves, and in wet, muddy, or otherwise disagreeable field conditions. Couldn't tell you if it's true or not, but my guess is that the crown is original. The military is very specific about specs for everything made for them. Given the sub seconds dial, I'd also guess it was issued to officers.
The crown is likely slightly more proportional than pictured as the pic appears to have been taken at a slightly wide angle focal length, perhaps the equivalent of a 35mm lens on a 35mm camera, making the crown appear larger.
From the reference section of the 3F watch library:
https://vintage-hamilton-wristwatches.c ... movements/
Off to a good start, man; nice catch.