One issue with the video at around 2:00 demonstrating gyroscopic effect is that the weight of the wheel is still in front of the axis so that weight is also causing the wheel to steer.Nice summary on self-stability (video):
Note that gyroscopic effect is a reaction to a roll torque. Once the wheel has steered inwards enough to produce a coordinated turn, the roll torque and the related gyroscopic effect become zero. As the wheel continues to steer inwards enough to start reducing (correcting) the lean angle to return to vertical, the roll torque becomes outwards, and the gyroscopic reaction opposes (dampens) the inwards steering needed for correction back to vertical. So the net gyroscopic effect is to dampen (oppose) the steering correction related to bike geometry.
It would have helped if just enough weight was placed behind the front tire to eliminate the weight related steering effect then note the reaction to leaning the bike with a spinning front wheel in mid-air, or to orient the bicycle nose down, but then the weight would tend to oppose any steering movement related to gyroscopic reaction.