Curious as to how you came across the Chalier method? Paul Chalier's method was a bit controversial in France at a time when some teachers were advocating use of all 5 fingers. I have also dabbled with many method books, and have come to the conclusion that with CBA most professional players develop their own fingering after a while. It really is a case of each to their own, and the choice of fingering is often influenced by the style of music preferred. You can waste a lifetime trying to find the "correct" fingering for every scale in the book, but when it comes to playing tunes we usually need to work it all out ourselves, as the scale fingerings advocated by the method authors are often of little use at all. Some method books also show what the author considers the best fingering for the tunes that form the exercises contained within them.
On several occasions when I have tried the suggested fingerings I discover that my hand ends up in an awkward position, probably because I have been playing for a long time and I had already worked out another way to play the tune concerned. Inevitably, I end up playing the tune my own way, always using as few fingers as possible, and usually with my thumb on the edge of the keyboard, which is an invaluable aid to accuracy, if not speed. Chalier's method was unknown to me until about 20 years ago, and I wish I had known about it sooner. I was told that Anzaghi's method was the only worthwhile one when I bought my first accordion, but like you it never suited me. Consequently, I wasted a few years learning the basics from a method book that turned out to be of no use to me. No doubt there will have been others who found Anzaghi's book invaluable, but that was not the case in my experience.
Chalier's book was written exclusively for CBA, whereas I have never been able to understand the logic behind the methods written by Manu Maugain, Galliano, or Anzaghi. The last two authors combine PA with CBA, and Maugain's method is entirely based on the "new wave" style, which seems to fly in the face of the older methods, which are more familiar to me. Another book in the same vein as Maugain was one written by Michel Lorin, which I found very awkward. His father, Etienne Lorin, was the author of a previous method book which I unfortunately found too technical and dry, and consequently never tried it out. The only method I persevered with was Medard Ferrero's, which ran into several volumes. I think I got into volume two before I heaved all the method books away and actually started playing. I never had a teacher so I just took things at my own pace. I probably got to about an Intermediate stage, but was able to play some of the more complicated musette standards. French musette is about as appreciated in Scotland as Eskimo culture is in the Sahara, so I was never really able to hone my skills to their full potential.
I haven't heard of the other two methods you mention, but all I can say is don't waste years trying to figure all the technical stuff. Playing tunes is a lot more fun.