Live center on the butt side works great. You can snug fit it into your box and cut a delrin or even plastic ring to let it ride on.. The other end , go to taig mill and you can get a spring loaded pointed center to use that gives you about 2 inches of adjustment there. This works great for your cues and holds very well.
As far as the drive pulley system. A chain drive is easy mounting it outside the hood facing up at the ceiling , cut a small oval hole in the side of your hood and run the chain thru to your fan. Any small fan blade will work. Just build a brace system inside the hood facing up as well, using threaded rod , cut down the end 2 to 3 inches to a smooth dowel, insert your blade onto it , using the threaded rod, run it thru your fixture and use 2 nuts tightened to each other on eather side. This will give you any height adjustment you may need and allow the fan to spin on your fixture.
The fixture can be made out of wood with some sealed bearing in it for your threaded rod to slide thru. Then hook your chain up to it(using a drive pulley) and their you are. Make sence?