I have a similar problem in our master. I was told I would need to run a conduit along the beam from the wall. I didn't want to do that because I didn't think it would look good. So no fan for me. You have an additional problem because the close mount fan on the smaller beam would make the blades come very close the the larger beam I think. Maybe you could put the fan with more of a drop in the wood ceiling part instead of the beam. Is there an attic above this space?

Don't know room size but probably you need a 52" fan to get the air moving.