Electronic band convergence can have a beneficial impact on thermoelectric performance, but finding the right band-converged compositions is still time-consuming. We propose a method for designing a series of compositions with simultaneous band convergence in the high-entropy YbxCa1-xMgyZn2-ySb2 material by zeroing the weighted sum of crystal-field splitting energies of the parent compounds. We found that so-designed compositions have both larger power factors and lower thermal conductivities and that one of these compositions exhibits a large thermoelectric figure of merit value in comparison with to other p-type Zintls. Our material shows high stability both thermally and temporally. We then assembled an all-Zintl single-stage module, nontoxic and free of tellurium, that demonstrates an exceptional heat-to-electricity conversion efficiency exceeding 10% at a temperature difference of 475 kelvin.