The ultimate method would be a crane. Crane to lift in a small excavator, a skip bucket then fitted to the crane to lift material out and dump it in to waiting tipper trucks. You'd probably be done in two days, including the footings and concrete for the extension. And the crane could lift in all your materials for the extension while it was there.
Other than that, a micro excavator might be able to make it's way through the house to dig and load up into barrows. But going the the description of the layout, I don't think that would be possible.
I'd rethink your whole approach and hold off any internal renovations until you've a full plan, and attack it in the right sequence. Speak to an architect.