I decided to video the problem at 60 fps with a high shutter (1/1300) so that I could slow it down frame-by-frame to get an idea of what's happening. While I'm not too familiar with the mechanics of a 35mm SLR design, it seems the shutter is indeed the problem. I shone a flashlight through the gate in order to highlight the phenomenon.
The following examples were shutter speeds of 1/500 and 1/000, respectively. I recorded each speed about five times, and the results were inconsistent. Not once did I get a full frame out of the shutter, and the ~ 30% shutter opening in the following examples were the biggest ones that occurred, meaning that any variation produced only smaller slights of light coming through, none with more.
500 shutter 4.jpg1000 shutter 4.jpg