Thank you all for the replies on my questions.
Our band plays the traditional way with fiddle, guitar, tit-fer and accordion. I love the sound of the accordion-bass.
For Nout: the other in the band have no problem anymore with the bass-notes of the Cajun accordion. They are used to it. And you're right anout Netty :-)
This is a funny coincidence.
Steve Riley put a photo on facebook from a new accordion he ordered by Eric Martin from France. It's a four-stopper key of C with three buttons more on the melody side. 3 additional buttons are from top: G# push/Bb pull, middle button is Eb push/C# pull, bottom is Bb push/F# pull.
They also built them like this for Quebec?
And also four Bass buttons.
Look at Steve's Facebook-page.
Great job from Eric.
It is true that the bass side will not harmonize properly a good part of the time.
As others have said, that bit of dissonance is part of what makes Cajun music what it is.
The best thing to do is to think of the bass side as part of the rhythmic accompaniment (like a drum), and not as harmonic accompaniment (like a rhythm guitar).
Just keep the rhythm going with the bass side, at least if you are playing in first or second position (C or G, on a C box). If you are in third position (F on a C box), the bass side is often left out because it gets in the way. Same with Pine Grove Blues or Danse de Mardi Gras.