Screw it, I’m not letting this thing beat me. Box 2 is in a shared wall with the garage. There is already some plumbing and wire running on the wall in the garage, so I’m going to tap a neutral out of a nearby garage socket and run in through a conduit in to the back of the box. From there I can run it to box 3 using the extra traveler wire and will be good to go.
Plan worked, so now everything is up and running!