There are 4 "cross bars" between the two sides of the reel. The clip is on one, and directly across from it are the sprocket holders. Instead of going THROUGH the center of the reel from sprocket holders to the clip, I was trying to insert the film into the clip and go AROUND the center cross bars.
Forgive this crude drawing. The four dots represent the "cross bars" between the two sides. The grey line is what I'm envisioning - over the sprocket holders, through the middle of the reel, and into the clip. The red line is what I was trying to make it do. In the clip, up and around the reel, and over the sprocket holders, and it just wasn't working.
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