Unless that lathe has tens of thousands of hours on it and was never lubes or had ways clean I have a hard time believing you have enough way wear to cause .200" variance end to end on work piece. In my way of thinking that lathe would have to have soft ways and been seriously abused to be that bad in the wear dept. I would do the two collar method, dialing tailstock in to get both collars to be within a thou or two, nothing fancy there. Then turn the whole piece end to end with a light cut , positive rake, sharp HSS bit, and see how big a saddle or hump there is in middle if any. .200" is a ridiculously large amount to be bed wear or saddle wear. I have seen more than my share of clapped out lathes, and turned on a few, never seen one that bad, I am betting you have a seriously out of position tailstock, or wrong tailstock, or bent tailstock ram, something is way out of wack and I would bet money its the tailstock.
Squeaking and intermittent cutting at beginning of cut would lead me think you may have the tool bit too high, maybe dull or very negative rake. You may have a combination of issues. I would rule one out at a time, make sure you have a nice positive rake tool bit, set on center, (use the trapped ruler method to check if that is all you have it works fine) after you know you have a good cutting tool then tackle the tailstock dialing in.