With the knobs installed on the cross beams, I could wire the 12V lights. All the wires are hidden by the channel molding serving as the cross beams and wall support beams.
I spliced all four interior lights to work from one plug. All the wires are taped inside the cross beam channels.
I tacked the vertical support beam to the wall with small dabs of glue, but the horizontal support beam and two cross beams are held in place with tension alone. The pieces can be snapped out of place if I ever need to address any wiring issues.
Once the roof is on, this wiring will be unseen but still accessible through the removable back wall. It would be a cramped space to work in, but it's better than having no access.
You can't see any of the channel wires from the barn door opening.