I purchased a Cylinder AND Control Valve from Rock Auto. Supplied by Lares Corp with Lifetime Warranty. Made in China. I will say that these are 100% made exactly as originals. Fit and work as expected. I had both my originals "reconditioned. Waste of $$. Lasted about 2 Years. You are working with 70 Year old Parts that were precision items when new but they are long past their "best before date". Don't waste your money fixing them.  If you want your  system to work as new buy new. I never regretted making the purchase of each of these. When the Power System works as it should there is no reason to update with a new integral System.

  

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I still say the problem is in the control valve.  if the spool does not center, they valve will send pressure to one side of the cylinder which will cause it not to center.  

I purchased a Cylinder and Control Valve from Rock Auto who is supplied by Lars Corp. They are made where else but China BUT they are a quality Product that fits and works as it is supposed to. Lifetime Warranty from Lars Corp. Rock Auto sells them for less than buying direct from Lars. I had both my original Cylinder and control Valve refurbished and both failed less than 2 Years later. don't waste your $$$ doing refurb. Buy New from Rock Auto. Don't forget the Originals are hitting 70 Years old. 

  

The non-centering return began after the new cylinder install and an exchange cylinder did not correct it?

When you remove the pump drive belt, the car centers itself?

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I am going to disagree with Klutz on the steering ram.  The Lars Corporation cylinder is very well made, and works flawlessly on 3 of my Mid-50 Ford vehicles.  I would suspect the problem is the control valve.  I have not tried any of the new reproductions so I do not have an opinion on those.  I use Precision Products in San Antonio Texas, but he is shutting down till the first of the year to move to a larger facility.  For Bendix-Eaton power steering used on Ford, Studebaker and American Motors vehicles.  I only use him and for my money he is the best in the business.  I would have your OE control valve rebuilt by someone who knows what they are doing and I think your problem will be solved.

Just a reminder to start the conversation ...

If the cylinder still leaks after a seal kit install, there is an internal seal that has to be replaced. The tube is cut open, the repairs done and then welded back  together

I would go this route rather than buying an off-shore sloppy copy.

Do you have a FORD WORKSHOP MANUAL? A DIAGNOSTIC ROUTINE WILL BE IN THERE.

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I spoke about this problem some time ago and have yet to find a solution to poor handling on my 1956 2-door Ranch Wagon.  I'll try to detail the power steering setup and maybe someone has had similar issues.  I took the power steering valve, ram and pump equipment off of another '56 and installed it on my car.  After many years, the ram began to leak and would not seal up, even with a rebuild kit.  I purchased a new ram cylinder, hoses and control valve.  Upon installation, the car would not always return to center, especially after making a right hand turn.  I spoke with the guys at Lares where I bought the control valve and they sent me a new one.  The issue still persists.  I added more positive caster to my alignment thinking that would cure the problem but it hasn't.  I'm running radial tires.  The steering seems to be ultra sensitive and that's why I increased the positive caster.  Finally, if I take the belt off of the PS pump, the car returns to straight ahead after a left or right turn.  Has anyone had this type of problem with a stock setup before?  I also have a '56 Sunliner with the same stock setup and it always returns to center after a turn and does not have that over-sensitive feel to steering.  Any  thoughts or ideas would be welcome and thank you.

Dean