Your take on the answer is very interesting, but I think you're looking too deeply for a simple answer.

One must realize the logo was chosen for just one movie, even if used for all three. (It was never originally intended to film three movies).

The marionette logo was used to show Vito's power. He was the marionette. He was the one pulling the strings. He was the one orchestrating what others did. He was the one who wanted to do this (and he suceeded).

Remember the scene with Mike and Vito in the garden ("Senator Corleone.... Governor Corleone...."). Vito used the literal value of the logo to explain his life to Michael. He said, " Fredo was -- well -- But I never -- I never wanted this for you. I work my whole life, I don't apologize, to take care of my family. And I refused -- to be a fool -- dancing on the string, held by all those -- bigshots. I don't apologize -- that's my life -- but I thought that -- that when it was your time -- that -- that you would be the one to hold the strings. Senator - Corleone. Governor - Corleone, or something".

The holding of the strings (the marionette) simply refers to who has control over others.