Welcome to the BSA A7/A10 Forum.
You are quite correct in determining the correct years.
1954 frame numbers started with CA7-101 and 1955 frame numbers began with CA7-7001 so frame number CA7-6400 is from 1954.
1955 A10 engine numbers started with CA10-4501 and 1956 engine numbers began with CA10-8001 so engine number CA10-5569 is from 1955.
I very much doubt that the bike will have have left the factory like this and I would suspect that the engine is a replacement.
FYI, the BSA Owners' Club (GB) will be able to check this out officially by using the original factory despatch records. If you wanted to go down this route I believe that you would get a certificate of authenticity that will also tell you the date that the bike was despatched and which dealer received it. There is a small fee for this and you don't have to be a member.
Beezageezauk.