Right, but do not forget you are inside your home, and unless you have Zen decorated house you will find your footwork messing with chairs, tables, sofa... you name it.
Of course stop an axe has to be difficult but with the so far personal choice of two short blades an axe can be "easily" handle like this:
unfortunately, there is no perfect solution to the scenario you're outlining. my first reaction though would be to throw a chair, lamp, whatever then follow up with a strike.
i think that the space issue you mentioned would work more against an an ax than a hammer. for instance if you have a doorway between you & the attacker he won't have many attacks available whereas you will still have several options.