"but bellows control IS what the aaccordion (etc) is all about!

Indeed! as I see it the bellows are to the box player what the bow is to the fiddler and should be taught/learned very early on as should a stacato fingering technique.

as to 'fine' bellows control on a big box Sir Jimmy Shand was the master of it on the 117 (yes 117) bass Shand Morino 3row box, using absolutely minimal bellows opening throughout the proceedings. In some ways the smaller the bellows the more movement is required to shift a similar amount of air accross the reeds wherea on a large box a very small amount of bellows movement & pressure will move a lot of air.

My view, for what its worth, is that the more extended the bellows are the harder work it becomes on the arm , neck & shoulder and the more difficult it is to exercise fine control whether this be to add 'shake' or to change note (on diatonics) whilst adding shake at same time.