Can I raise a sagging shed roof by winching the walls back into place?
Your plan is exactly right, except that you don't need such heavy-duty hardware to do the jacking/winching. Even a pair of motorcycle ratchet straps or a come-along is going to do the job, especially if you jack up the ridge board. I think it'll all move easier than you anticipate. Just make sure you have solid connections to the walls so you don't have any sudden surprises if something lets go. Maybe lag some loops to the top plates. 

One or two rafter ties, well-attached, will prevent the problem from happening again. You could probably get away with keeping them a foot or so above the wall plates, too, if headroom is at a premium.

Good luck.