If the "wobble" is caused by the faulty brake disc mechanism (the friction disc that prevents the hoist from running away on the way down), an electric friction wheel drive WON'T fix the problem. The friction disc still needs to be functioning properly for the electric friction drive to work.
If the winch is "jumpy" going down, but smooth going up, it's probably the brake disk and a good cleaning (maybe disk replacement) as mentioned above should help. If the handwheel shaft is sloppy (wobbly) in its bearings/bushings that's a different story. Or it could just be the handwheel itself has the bore worn out, and is a sloppy fit on the input shaft. If I remember right, the bore of the handwheel is threaded onto the winch input shaft, that's part of how it opens and closes onto the friction disc. The threads could be worn. There probably should also should be a compression spring near the outside of the handwheel attachment to the input shaft.
From the outside in: Hex head screw, washer, compression spring under the washer, then handwheel, then onto the input shaft, with the brake disc and a thrust washer along with an external toothed thrust washer, behind the handwheel. The spring might have been plated steel when new, but over the years they can rust, break, fall off, etc.
I think the principle of operation is:
Going up, the handwheel should thread towards the winch and pinch and lock the brake to grab the toothed washer, for a positive drive input to the winch shaft all the way up, clicking the ratchet/pawl all the way up.
Going down, the handwheel slightly unthreads away from the winch, letting the brake go slightly loose and the toothed washer stays stationary against the pawl, and if the lift/winch tries to run down faster than you are spinning the hand wheel, the hand wheel/input shaft threads close back up and put pressure on the brake disk and the toothed washer (against the pawl), and the dropping load stops until your handwheel input is faster than the winch falling (loosening the brake disc again.)
I got lucky when I found my 5000 lb boat lift on craigslist, it was already set-up with 12 volt direct drive from the manufacturer, with a solar panel. All I had to add was a solar panel charge controller so the solar panel didn't "overcook" my new battery. $20 for a 5-45 watt Battery Tender solar controller, sits inside the battery box. The direct drive is a different concept, no brake disc, no external wheel. It's a worm drive input which by it's own principle of operation cannot run away from the input. No clicking noise up or down.