Cool...
I will not hold you to your hat offer.
Give me a few minutes to draw up a supporting diagram..for now, here's a graph to consider, it shows the dissipation differences between a mono and a biwire configuration..
Ok..now with that to see, a little splainin...
The currents and the resistance are normalized, so the peak woof and tweet currents are 1, and the resistance of the wire is also normalized to 1.
The woof current is the blue line, the diss is (Asquared) I<sup>2</sup>R, so as you can see, it peaks at 1, and is always positive (real dissipation cannot be negative). It is your basic sine squared waveform, a direct result of the woof current flowing through a wire by itself. Note that for an ideal load, this is also exactly the same dissipation time profile scaled differently.
The tweet current is the magenta line, called Bsquared. again, I squared R...
With biwiring, the total wire dissipation is of course, the sum of the two, A squared plus B squared, and the load dissipation at the speakers is an exact scale of the wire dissipation.