The documentation of axes.table says

[...]
kwargs control the :class:`~matplotlib.table.Table` properties:

  [...]
  zorder: any number

but if I call

t = ax.table(..., zorder=1) 

I get the following error

TypeError: table() got an unexpected keyword argument 'zorder'

However

t.set_zorder(1)

works as expected.

I think that either the doc should be fixed or matplotlib.table.Table should accept and use zorder.

I haven't tried other kwargs.