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.