I just read the reviews of the Harbor Freight Bicycle Lift. Some people believe the rope is inferior to what's needed and one guy suggested swivel pulleys would be an improvement and another recommended increasing the bend angle of the hooks , but the reviews were sufficiently positive to convince me to get one as soon as I can get to one of their stores.
So, that's what I'm gonna do, make a beam supporting structure, get the Bicycle Lift, replace the rope, and install. I consider further improvements later.