Nick,
I totally agree with the first paragraph of your last post. There is little difference in the power requirements between two closely spaced 2-blade coaxial rotors, and a 4-blade single rotor; if all the blades are identical in span, chord, rpm etc. etc.
However, there is a large difference in the power requirements between two widely spaced 2-blade rotors and two closely spaced 2-blade rotors. In other words, as the two separated disks approach each other (vertically, horizontally, or diagonally in the case of the Tandem) their slipstreams experience an increasing overlap and the power requirement increases.
This is the supporting [Blade Element Theory] data for the above sketch.
The power requirements for the Interleaving, the Intermeshing and the Tandem will be somewhere between these two extremes.
Dave