Thanks for so patiently making this video, I admire your perseverance! What you were experiencing is strange because the tape is driven by the capstan and pinch roller and not by the larger take-up reel. The take-up reel can spin without affecting the tape movement, it’s only there to take-up the slack. Therefore a loose loop *should* work (not too loose) and so it seems like you might have a problem with you capstan and pinch roller. Perhaps the pinch roller is too smooth and not gripping the tape. Thanks for sharing a very well put together video, I enjoyed it. Hope you do some more!
Adding a tensioner wheel would help. Borrow one from another cassette, find the ideal position, mark it, glue the wheel in place. I doesn't matter that it won't turn.