Weird 4-way wiring

Took me forever, but I think I figured out the wiring for a 4-way in my home. The N.C. wires do not appear to be attached to the panel or anything else. Is there any way to wire this up with a smart switch (on/off is all I need, but I do have dimmers that I can use if I need to. I have the red versions of both)? The problem is that I don’t seem to have both a hot and a ground in the same box anywhere. I don’t mind using either dumb switches or aux switches for the other 2.

The problem with that wiring diagram is that there is no neutral in box 1.


Do your travelers have a white wire? you show black and red so unless your drawing chose different colors, there should be a white in each cable.