Only A, B, and C are available at any time. To read the other buttons, you have to toggle a select line multiple times. Each time gives you another part of the packet. A six button controller uses the initial controller word plus three extra words to send the controller ID and extra button info. This is all controlled by the uprocessor in the controller - you don't have direct access to the button lines... not unless you wish to cut the lines from the control board and add your own processor (like a PIC).
The method shown in the ADoomPPC readme (done by yours truly) is the most straightforward way to read a SEGA six button controller. It only requires one simple hardware mod, and then a routine to read the controller packet. Anything more and it would just be easier to replace the SEGA control board with a PIC chip. Then you could do whatever you wanted with the buttons and how they were sent to the Amiga.