In some ways, the MSSM seems promising as a framework for tHWZ numerology. The reason may be seen at the end of section 3.4 in Stephen Martin's primer: susy determines the couplings of the scalar potential, in terms of coupling constants elsewhere in the theory. If I am interpreting that passage correctly, the quadratic coupling will be set by the top yukawa, and the quartic by the gauge couplings.
However, the MSSM has a lot of annoying particles like gauginos and sfermions which get in the way. Here last decade's ideas about split susy are useful. In particular, in section 2.3.3 of "Predictive Landscapes..." we read about a framework midway between split and supersplit susy, in which only the Higgsino is light. That sounds worth exploring.