Rear end:
Are you really sure that it is a Dana 44? It is very difficult to see the difference between a Dana 44 and Dana 45.
All 1955 and 1956 Mercury passenger cars used the Dana 45.
The best way to identify them is to look at the casting at the right lower web close to the cover.
If the number is 45 its is a Dana 45, and if the number is 44 it is a Dana 44.
At the left lower corner of the cover a tag should be bolted which identifies the axle ratio, two numbers, ring and pinion count.
Transmission:
1955 Mercury used the stronger BW T85 with R11 overdrive. 1955 Ford used the weaker transmission.
Problem solved, that is the important thing
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1955 Mercury