We report on Rayleigh-Bénard convection with strongly varying fluid properties experimentally and theoretically. Using pressurized sulfur-hexafluoride (SF6) above its critical point, we are able to make measurements at mean temperatures (Tm) and pressures (Pm) along Prandtl-number isolines in the (T,P) parameter space. This allows us to keep the mean Rayleigh- (Ram) and Prandtl number (Prm) constant while changing the temperature dependences of the fluid properties independently, e.g., probing the liquidlike or gaslike region that are left and right of the supercritical isochore. Hence, non-Oberbeck-Boussinesq (NOB) effects can be measured and analyzed cleanly. We measure the temperature at midheight (Tc) as well as the global vertical heat flux. We observe a significant heat transport enhancement of up to 112% under strong NOB conditions. Furthermore, we develop a theoretical model for the global vertical heat flux based on ideas of Grossmann and Lohse (GL) in OB systems, adjusted for nonconstant fluid properties. In this model, the NOB effects influence the boundary layer and hence Tc, but the change of the heat flux is predominantly due to a change of the fluid properties in the bulk, in particular the heat capacity cp and density ρ. Predictions from our model are consistent with our experimental results as well as with previous measurements carried out in pressurized ethane and cryogenic helium.