This all is very interesting and i didn't know anything about all those different systems. Am I right if I say that each row on a Irish have a diatonic scale, but together with the other row you have chromatic possibiities?
CBA or Chromatic Button accordeons are also known as Continental Chromatics.
They come in "B" systems or "C" systems. also known as B Griff or C Griff.
They are usually 4 row or 5 row.. I have seen 6 rows but these were the Russian versions known as BAYAN.
These are not diatonic.
If I were starting accordeon all over..I would start,and stay with a CBA.