How to minimize peak-to-peak amplitude of periodic waveform through FFT phase shifts?
There are algorithms for determining low-peak-factor signals, for example:


  "Synthesis of low-peak-factor signals and binary sequences with low
  autocorrelation (Corresp.)", M. Schroeder, 1970


I have used this for flat-spectra signals to minimise peak to peak amplitude.

However I think this may be an XY problem. Do you have a limit on how much distortion you can introduce to the signals? Have you tried using a dynamic range compression algorithm? There are limiting algorithms which can increase the RMS amplitude significantly without introducing significant audio artifacts.