I used a chart like yours too for a while. After the instructor completed Boolean algebra and tested us on it, we weren't required to use it any more. At that point Karnaugh maps became my good friend! I guess that marks me as an engineer...
Like you I order my chart as a mathematician, engineer or programmer would ...
I found the following counting method most useful as it worked best with K-maps. In fact, this is the table I sketched into the front cover of my digital circuits textbook :)
|A||B||A or B||A nor B||A xor B||A and B||A nand B|
-- Yeah, I'm a Delt.