Edit: Math is off, gonna redo, all below can be taken as wrong.

Woah, you're spot on.

The numbers work out. 17 and 22, with both old and new interpretations of the paths.

Damn, I feel like I'm going full bonkers now.

Original 17 paths:

1-2, 2-3, 3-5, 5-8, 8-4, 4-3, 3-7, 7-1, 1-8, 8-9, 7-6, 6-4, 4-1, 1-5, 6-2, 2-8, 1-9

Later 22 paths (actually a devolution):

1,2,3,5,8,4,3,7,1,8,9,8,5,6,4,1,5,6,2,8,1,9

Thus, in the year 1516, Reuchlin's diagram came to appear on the cover of the Paolo Riccio's Latin translation of Joseph Gikatilla's Gates of Light. The diagram only had 17 paths and, at the time, the concepts of 10 spheres and 22 letters were still distinct in the literature.

https://en.wikipedia.org/wiki/Tree_of_life_(Kabbalah)