We report measurements of electrical resistivity under pressure to 5.8 GPa, magnetization to 6.7 GPa, and ac susceptibility to 7.1 GPa in KFe2As2. The previously reported change of slope in the pressure dependence of the superconducting transition temperature Tc(p) at a pressure p*~1.8 GPa is confirmed, and Tc(p) is found to be nearly constant above p* up to 7.1 GPa. The T-p phase diagram is very sensitive to the pressure conditions as a consequence of the anisotropic uniaxial pressure dependence of Tc. Across p*, a change in the behavior of the upper critical field is revealed through a scaling analysis of the slope of Hc2 with the effective mass as determined from the A coefficient of the T2 term of the temperature-dependent resistivity. We show that this scaling provides a quantitative test for the changes of the superconducting gap structure and suggests the development of a kz modulation of the superconducting gap above p* as a most likely explanation.