My son has a gantry in his shop. His has 9' under the beam height (has to be careful moving the gantry around the overhead lights in his shop). He started out with a chain fall, but soon discovered it cost him too much space under the beam. He then bought a 1500lbs rated electric winch from HF to hang from the beam, which still puts a limit on how high he can lift something (that long reach operating box on the electric winch sure makes it easier to lift or lower stuff, with the chain fall, he always had to climb in to pull the chain straight up or down and then fight with where the excess chain was).
He is mostly using his set up to pull motors, but I suspect the under the beam clearance on a cab lift would get pretty short pretty fast. You will loose height when you add the chain fall, and you will loose more height when you add the scale, you will also loose some height with what ever method you use to lift the cab. Then you need to be above the cab to operate the chain fall. You might want to determine how much height between the cab and the bottom of the beam you will need, before you can move the cab away from the frame, and place it onto the next frame.
When I lifted cabs off frames, I had to put my cherry picker (engine hoist) on the inside of the cab (along with a 4" x 6" wood beam) in order to gain the height I needed to lift the cab, and then I was still at the max height my hoist would go. I needed to lift the cab floor at least 12" above the top of the transmission before the cab's rockers cleared everything.
Just a heads up from a guy that found this stuff out the hard way.