Firstly, this fiddle shows the problem which you describe.
As yet, I don't know how to get around this, but it seems like the spec hints to this here:
The computed values of ‘overflow-x’ and ‘overflow-y’ are the same as
their specified values, except that some combinations with ‘visible’
are not possible: if one is specified as ‘visible’ and the other is
‘scroll’ or ‘auto’, then ‘visible’ is set to ‘auto’.
