I wanted to update the thread. I've been looking at the existing
ceiling fan for the longest time and I think I finally figured out what
they did to wire it . . . after posting on the Internet.

My original description of the beam is wrong. It isn't at the apex of
the ceiling. Rather, it's about halfway up. So you'd have one side of
the beam more exposed than the other, right? Well, on the side with
more exposed, it looks like they had boards running across that jut out
off the beam. I'm betting they're running wires behind it.

I'll have to see if this is that channel material that has been
mentioned already. Given 2/2 suggested that, I would imagine so.