If the fan is simply maintaining greater than ambient pressure on the sail, the flow rate forward through the fan would be reduced due to that increased pressure. It would have to pull in only enough air to replace the amount of spillage from the sides of the sail. I think we agree, and the experiment agrees, that this does not produce forward momentum.That is totally trivial. The discussion was about the net force on the boat, not just on the sail.
When the fan is directed to the side, the pressurized volume of air between the fan and sail would be pushed backward from the sail and the sail and boat pushed forward. Whether that will be greater than the forward flow through the fan at that point is difficult to say without some measurements. That is why I suggest turning the fan off. But it does appear to be enough to cause a bit of forward momentum even with the fan on.
Better still would be to have the fan push air into a balloon, build up the pressure and then turn the fan off letting the air in the balloon shoot backward. That is essentially how a jet engine operates, except that it draws air in from in front so it can operate continuously.
The boat doesn't move.So what happens in the video where the fan always points the same way?