You should find out what engine you've actually got, and what model the '55 parts are from.
If the '55 drivetrain parts aren't from another T-Bird that makes them generally less usable.
As delivered there were several changes between '55 and '56 T-Birds,
and in the 60 years since new, many things could have been swapped with something else.
It's common for T-Bird engines to have been in & out of the car a few times, and the chances of the '56 being 'original' are fairly small.
The '55 T-Bird engine was a 292 4bbl. A '56 could be a 292 4bbl or a 312 4bbl (with more options).
A 3 speed manual transmission; they may(?) be the same between '55 & '56. There was an OD option.
The '55 / '56 automatic transmissions can have a different style cooling system.
Various T-Bird specs & gear ratios are listed in the 'mileposts' links below, the rear axle housing is the same in '55 & '56, but not '57.
The '55 & '56 T-Birds had similar but different; carb, intake manif, and distributors. Those individual parts are not interchangeable between the two years, unless you keep them together as a 'set'.
In '57 those parts, and more, were upgraded again.
A drivetrain from a full sized '55 Ford is not a bolt-in swap into a T-Bird. There are more than a few T-Bird specific parts for the engine, and I believe the transmissions are a different case size & length. The rear axle housing and/or spring pads may(?) be a different width.
A non T-Bird '55 y-block engine would most likely be a 2bbl 272.
Here are a couple links to start looking at.
Check the casting numbers on the engine blocks to help figure out what they are/might be.
The block casting number should be just above the oil filter, or at the base of the distributor.
http://ford-y-block.com/technical.htm
http://automotivemileposts.com/tbird/prod1956tbird.html
http://automotivemileposts.com/tbird/prod1955tbird.html
http://www.portholeauthority.com/thunderbirdETC/tbird/tbirddesc.html
You can post a reply with pictures of anything you're not sure of.
.