Information content of amplitude modulation versus single-sideband transmission
Are you not "just" describing quadrature (I/Q) modulation? OTOH I admire that you came to the conclusion by yourself, without (consciously) thinking about I/Q.

From the Wikipedia article


  Like all modulation schemes, QAM conveys data by changing some aspect of a carrier signal, or the carrier wave, (usually a sinusoid) in response to a data signal. In the case of QAM, the amplitude of two waves, 90 degrees out-of-phase with each other (in quadrature) are changed (modulated or keyed) to represent the data signal. Amplitude modulating two carriers in quadrature can be equivalently viewed as both amplitude modulating and phase modulating a single carrier.