If I was closer I would go for it, I wouldnt mind having a spare to rob parts off of.  But me being here in Texas, that would be a long way to travel to pick up a transmission.  Mine is aircooled as well so it would be basically identical to mine.  Seems like for the '56 model year most were water cooled and the aircool was a bit of a oddball for '56 but was common for '55.

1956 Ford Fairlane Town Sedan - 292 Y8 - Ford-O-Matic - 155,000 mi

In 1961, they converted to Type F

TYPE-F was not released until the 1968 production year.

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Regarding the issue of transmission fluid Type A, Type F, Dexron, Mercon, etc., when the Fordomatic came out in 1951, it used Type A fluid. In 1961, they converted to Type F. The friction plates in the earlier transmissions were a metallic composition and by the time they changed to Type F, they changed to various forms of composition material. Around this time, General Motors changed their fluid to Dexron which evidently had more friction modifiers in it than Type F. The drawback to Type F is it does not lubricate as well as Dexron or Mercon. Thrustwashers, metal seal rings, bushings do not last as long with Type F. Ford in 1979 sent a Service Bulletin to their dealers to not use Type F in their transmissions any more. In 1976 they had changed with the C-6 to a different fluid and they called it Type CJ which was basically Dexron II. In 1979, the reason they stopped using Type F, was that in California, Granadas and Monarchs, because on those cars the catalytic converters were on each side of the transmission and in southern California, unless you live in the mountains, it normally doesn't get below 40 degrees. Because of the placement of the catalytic converters, there was so much heat generated by them that the fluid would turn brown instead of red and it lost its ability to engage the intermediate band. When you would drive the car, it would slip from first to second to third like a Buick Dynaflow. The only cure for this was to pull the transmission and replace the intermediate band and the direct clutches and to clean the transmission internally because the fluid would build up deposits that looked like mud, sometimes it would plug the filter and then the car wouldn't even move or it would make terrible noises of trying to pump the fluid through the filter. The reason I know this is that I worked at Ford dealers doing automatic transmissions from 1965 to 1995 and saw what happened to transmissions that used Type F. In addition, the governer with a spring in it was an aftermarket fix because if you set the engine idle speed too high, when you would come up to a stop, in the last little bit before you came to a full stop, it would clunk when it downshifted at a very low speed. So if your idle speed was set at 550 rpm in gear, you would get this issue when you came to a stop. I remember when I was younger, older people who had been used to driving cars with a standard shift, they wouldn't like for their car to creep at a stop light. So a lot of these cars had very slow idle speeds of 450 or 475 rpm and they didn't notice the clunk coming up to a stop. Just another opinion after working on these things for 30 years.

Rusty, if you or anyone else is interested I have the Ford-O that was removed from 56 when I installed a 62 CruiseOmatic. The tail housing and torque converter are not with it. It’s air cooled and free to anyone wanting to pick it up. It has about 6000 miles on a rebuilt by the previous owner. Worked perfect but I wanted a 3 speed all the time without doing whatever you needed to do for that to happen. And I’m not interested in whatever it is.
I live in So Cal

56 Vic, B'Ville 200 MPH Club Member, So Cal.

mercon is now the trans guys at ford dealers sware by, had a old Mercedes with  slippery shifts, on the advice of the ford trans guy drained the trans and filled with mercon. shifted way better, no slippage.

No, it is not going to be solved until everyone comes to a basic reading comprehension understanding. You could present pages of TECH but there will always be a few that will not believe what the facts are.

GM and FORD went their separate ways regarding fluids beginning in 1959. DEXRON and  MERCON are marketing names only. You have to understand how to read and cipher API ratings and what a particular manufacturer calls out for a specific application (and subsequent changes/upgrades).

A statement such as 

Type A was originally used to provide smoother shifting. However, smoother shifting usually results in more slippage, which leads to overheating and premature failure. Ford that reason, Ford stopped using Type A and went to Type F

is an example of not understanding the principle. How this argument keeps going on over and over when a simple search will give one the information needed is beyond me.

FORD as well as some EURO manufacturers still use TYPE-F in some applications. This is why FORD still offers TYPE-F.

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This question about fluid is not going to be solved.  Several people think that Type F stands for Ford when it actually is just a letter designation.  Years ago I was tech editor for a national car club and was asked the question about Dexron or Type F for the cars.  I spoke to an oils engineer at scrubron (educated in these things far over my head) and he told me that the Dexron was the closest fluid to the Type A, Suffix A fluid that was used in the 1950's  If you go by the logic, all US manufacturers of automatic transmissions specified Type A, Suffix A fluid.  Since scrubrolet used the same fluid, it would then be logical to say that Type F should be used in the Powerglide or Hydromatics of the day.  Of course, since Dexron is used on later GM cars, Dexron is what most people would put in an early GM automatic.  I had a Ford mechanic tell me that type F is the correct fluid and anecdotally said he has used it for years with no problems.  I suspect that either will work.  The Engineer gave me a detailed explanation for the Type F having to do with friction modifiers and the later (late 1960's into the 1970'a Ford transmissions needing a harder lockup shift and that is what the Type F is supposed to accomplish.  You are correct but the argument will never end.

Ford also changed the clutch material as well.

The use of Type F in a Type A system will from every source I have came across to date will prematurely wear out your clutches. 
Its why on original setups its best to use the proper fluid unless you have had it built and know the clutches can handle the fluid

TYPE F can be used in a TYPE A / DEXRON application. TYPE A / TYPE A SUFFIX A / DEXRON cannot be used in an original TYPE F application unless friction materials are updated.

TYPE A / TYPE A SUFFIX A (FORD different blending from GM 1959/ ) was used by FORD until the 1968 model year and beyond actually. TYPE F was designed to be a LIFETIME FLUID, that meaning once out of drive-train warranty.

GM DEXRON is a design progression from original GM TYPE A SUFFIX A as was 1959/ FORD fluid

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I would not use Type F unless you intend to go racing. Type F will firm up shifts but lacks the protection and longevity of Dexron.

Ford also changed the clutch material as well.  The use of Type F in a Type A system will from every source I have came across to date will prematurely wear out your clutches.  Its why on original setups its best to use the proper fluid unless you have had it built and know the clutches can handle the fluid.  Like my C6, it calls for Dex/mer fluid but after rebuild majority will cite to use Type F now.

1956 Ford Fairlane Town Sedan - 292 Y8 - Ford-O-Matic - 155,000 mi