The 6 foot spacing you’re using is from the paper you referenced. My value of 4 foot is a calculated value from a combination of the chart and the calculator I linked in my post. It’s for climate conditions in Michigan rather than those of New York state which your paper is based on. There are two other differences. First, I am using sprinkler irrigation “as needed” instead of carefully monitored drip line irrigation. Second, Fuji is a much higher vigor scion than GoldRush. If I redo the calculation for a Fuji scion with drip irrigation I get a 6 foot spacing too.
In the paper you referenced, the trees are trained to the vertical axis system which is similar to the tall spindle system. These trees are supported by a trellis. In these systems you crop earlier and don’t build a lot of wood that can be used to produce a self supporting tree. The training methods and the early crop “runts the tree out” to a certain degree. This allows the tree to be kept in a small space with minimal pruning.
For a self supporting tree you build a lot of wood and produce a self-supporting tree with a strong framework using a central leader training system which means the tree fruits later in life. The central leader produces a big tree that doesn’t need a stake but it’s going to require wider spacing unless your willing to do a bunch of heavy pruning.