Prior questions have established that the 5th Edition iteration of Tenser's Floating Disc can move around obstacles, but will not move (or even exert horizontal force) when it does not have a legal path to a position within 20 feet of the caster. Therefore:
Suppose an enterprising wizard were to commission the construction of a structure on an empty field. The structure consists of a spiraling ten-foot-tall wooden wall or fence, with an outer radius of 100 feet, an inner radius of 20 feet, and a distance between each loop of 5 feet, thus creating a spiral corridor 5 feet wide and about 6000 feet long. A gate is placed at the outside opening of the spiral, and ladders and bridge over the structure allow the wizard to climb up and over the spiral to easily move from the outside to the inside.
The wizard, who has no sense of right and wrong and therefore has not tested the following procedure at all, then offers any curious onlookers an exciting experience for a modest fee. The wizard casts Tenser's Floating Disk while outside the spiral and has the attendee seat themselves upon it. The wizard then climbs the ladder and traverses the bridge until they are in the center of the spiral structure. Then they signal to an assistant stationed outside the spiral wall, who opens the gate. At this point, the floating disk has a path to a space within 20 feet of the wizard which does not violate any of its movement constraints.
Does the disk move along the spiral path, and if so, how quickly?