Hi,
I just stumbled upon this thread, and it looks like you did some incredible work here. A couple things, you probably already know. There obviously were two types of shots in the song. In the close up shots, where Jim wasn't under the water in a tank on the Universal lot. Jim controlled the puppet's mouth and Kermit's left "playing/picking" hand. Another puppeteer controlled the motion of Kermit's right hand going up and down the neck of the banjo/frets.
In the long crane shot push in shot, (yea it was crane even though it was only a foot or so above the water. Kermit's mouth is controlled by Jim with him in a tank under the log, under the water. Kermit's left hand doesn't move and his right hand is controlled with a servo. But most people thought it was a hole in the banjo, but it was controlled via an armature that went around the back of the banjo.
In the medium close up shots (where you pan down to show all of Kermit), Jim is controlling Kermit's mouth while in a tank, under the log, under water. But both hands are controlled remotely with servos. The one thing Henson was never happy about (besides spending two days in a tank) was that banjo always look too deep, and it didn't move like it was a free object, because it was locked down to Kermit/The Log. But that was to accommodate the servos.