How to get electrical from the side of a beam into a wall under it without crown moulding?
It sounds like you're suggesting drilling the beam clear through from top to bottom, or notching the side of one of the outer 2x8s from top to bottom.  Neither of these are allowed under modern building codes and they significantly compromise the capacity of the beam.  It's like subtracting one of those 2x8s from the beam.
With that said, I previously owned a house where water supply pipes had been inserted top-to-bottom through a structural beam, and the house had not fallen down 30+ years after it'd been done.  Thank goodness for safety factors!
Instead, build a chase
If I were you, I would build a small chase to bring the wiring from the joist cavity into the wall.