Managing user defined and default values for instance attributes
Some minor comments on the code:


Class definition should be separated from the line with import by two spaces.
My personal preference is to have key-value pairs in dictionaries separated with a space after colon as shown in PEP 8: 

defaults = {'A': None, 'B': 0, 'C': 0}

Comparing to None should be done by is instead of ==:

required = [key for key, value in defaults.items() if value is None]


Note that I also removed redundant brackets around key, value.  There are several other lines where brackets are not needed around them.
PEP 8 also discourages aligning several lines with assignments by =, so instead of, for example:


results        = None
keys, values   = zip(*setup.items())



it should be

results = None
keys, values = zip(*setup.items())

There is no need to specify object in class O(object), class O will work fine.
Here:


for key, value in kwargs.items():
    if key in setup:
        setup[key] = kwargs[key]  # user specified overrides default



you don't use value, but you could:

for key, value in kwargs.items():
    if key in setup:
        setup[key] = value

Here:


  keys, values   = zip(*setup.items())


you don't need values as you overwrite them later. So, I'd just remove this line altogether.
set((1,)) can be replaced with {1}, and set.difference can be replaced with just -. BTW, I like how you combined two conditions from my previous review in one!
Don't forget to use np.can_cast instead of checking the dtypes against np.int64. The current version failed for me until I changed it.
[array.astype(float) for array in arrays] can be written as list(map(np.float64, arrays)) but both versions are fine.
The overall design looks quite unusual to me. If it would be me, I'd separate validating data from the container that will keep it. In other words, I'd not keep it in one class. BTW, if a class has just two methods and one of them is __init__ then it shouldn't be a class. Another thing you could try is pydantic library. Never had a chance to try it myself though, but with this problem of data validation I'd give it a shot.