Here's a couple pics of my elevator, should be pretty easy to run a similar setup without a gearbox, just mount a jackshaft from one side to the other with a couple of bearings, and gear reduction as needed/wanted. If I were building it, I'd go with chain drive on one end, and belt drive on the other. Chain for durability (run this on the final reduction - there will be more torque there than on the first reduction), and belt to have something to give if things jam up. I have a slip clutch on this setup, but it might not be cost effective for you to add one.
Got any farmers around with a "Bone Pile" out back? Lots of options and pickings of shafts, chains, sprockets, gearboxes, etc. available for maybe not much more than asking.
I need to drag this thing out of the weeds this spring, shorten it up, lose the drag hopper, and put a hydraulic motor on it to run it. After my splitter gets redone, it will run off the splitter hydraulics. If I need to use it before that, I have some long hoses I could run from the tractor to it. (The tractor PTO is already running the splitter.)