I went through the same scenario last year with a 1961 5.5 Johnson Twin. Great engines. Yours is basically the same style as mine, but about 1960, they went from the round case to a '60's "tail-fin" look like the cars had.
Several things I learned: To drop the lower unit(which you should do) and change the water pump impeller AND the fat "O"-ring seal around the shift rod, you have to pull the power head to disconnect the shift rod. A major pain in-the ^ss! To replace the shifter rod seal, you have to get the brass seat out. Videos on the Internet for that. If you don't change that, you WILL get water into the lower unit. Most of the parts you will need are available through marineengine.com.
If yours is a '56, it's an AD-10, '57 is AD-11, '58 is AD-12. But marineengine.com calls the '57 a Model 7522.
I fought a problem on mine with running on one cylinder intermittently, until I took out the points and condensers and replaced them with two electronic sensor modules. Mine were made for Kawasaki, but there's a lot on the market. About $20. Those solved my problems immediately. Now, my 56-year-old motor runs like a top.
Goog luck! IslandJim
I'm an Eighth Day Adventist. On the Eighth Day, God went fishing!