The "working distance" as you put it cancels out. Think about focus and the opportunity to be out of focus as a cone of confusion. The cone comes to a point at where the picture is in focus, which in the case of a 1:1 macro will be 2x the focal length from the effective aperture of the lens. The cone goes from a point in focus to the aperture. Anything inside that cone will add something to one particular image point.

Given that view, consider what happens as the focal length is doubled. The distance from the cone point to where its outer edge is defined is doubled, so that would make the cone narrower. However, you said the f-stop is held constant, so the aperture diameter is also doubled. You are now back to the same cone of confusion as it leaves the object, just that it is longer before it gets to the lens. Since the cone angle is the same, objects in front of or behind the focus point will be out of focus by the same amount. Therefore whatever threshold of blurriness you decide is still in focus will occur at the same distance from the object being photographed, so depth of field is the same.