There's a fundamental difference between the speakers in the Tech Ingredients video and what you're doing. In the video, the foam panel is being used as the speaker "cone". They are not really "speakers" in the conventional sense, they are drivers hanging in the open air. Those flat panel open back speakers are great if you hate bass, because you'll never hear it from open-air drivers like that.
But you are not mounting a large flat foam board to a speaker coil, you are using foam board to build a speaker enclosure with a conventional bass driver. Foam board is not rigid enough for this, as your testing showed. When the speaker cone moves out, the cabinet will flex inward, so you'll have weird phase cancellations. The speaker driver and cabinet will actually work against each other.