There is only one small difference between SSD1306 and SH1106: The SH1106 controller has an internal RAM of 132x64 pixel. The SSD1306 only has 128x64 pixel.
First problem for standard 128x64 OLEDs with SH1106 controller is: How is the 128x64 window mapped into the 132x64 RAM?
It seems, that the 128x64 OLED is centered in most cases within the 132x64 area, that means pixel (2,0) in ram is pixel (0,0) on the display.
For u8glib, the update for the SH1106 was very small. I just had to shift the display by 2 pixel. This is more complicated with the Adafruit lib. Mainly the procedure "Adafruit_SSD1306::display(void)" depends very much on the hardware architecture and assumes, that the width of the RAM area is 128 (which is wrong for the SH1106). I think the procedure Adafruit_SSD1306::display(void) needs to be rewritten completly (including the commands, which are sent).
Oliver