Field ionization measurements of high-n CH₃I and C₂H₅I Rydberg states doped into krypton are presented as a function of krypton number density along the critical isotherm. These data exhibit a decrease in the krypton-induced shift of the dopant ionization energy near the critical point. This change in shift is modeled to within ±0.2% of experiment using a theory that accounts for the polarization of krypton by the dopant ion, the polarization of krypton by the quasi-free electron that arises from field ionization of the dopant, and the zero point kinetic energy of the free electron. The overall decrease in the shift of the dopant ionization energy near the critical point of krypton, which is a factor of 2 larger than that observed in argon, is dominated by the increase in the zero point kinetic energy of the quasi-free electron.