The effect of strong scintillation conditions on GNSS transionospheric paths of propagation is further investigated employing the most recent update of the Hybrid Scintillation Propagation Model (HSPM). The variation of various parameters including spectral indices and other statistical moments of the field is studied as a function of the severity of the signal fluctuations. The correlation time of the complex amplitude of the field is found to rapidly decrease as the scintillation severity increases, but by contrast, the intensity correlation time stays almost constant over a wide range of S-4 showing only slight decrease in the model's range of validity. The dependence of the spectral indices of both phase and amplitude on S-4 is also determined, and the spectral index of the phase fluctuations tends to 2 for the most severe scintillation, as expected from both experiment and theory. The effect of "canonical fading" is also studied, when, in the conditions of strong scintillation, fast phase changes occur along with deep amplitude fades. The probability of the effect of the "canonical fading" is studied for the conditions of strong scintillation, and the mean time between cycle slips shows a significant decrease as S4 increases. A comparison is also presented between calculated results of S-4, spectral indices, and the correlation radii of the complex field and field intensity, utilizing both the HPSM and equivalent phase screen model for both weak and strong scintillation conditions. These show the differences that can occur which can also depend on the equivalent phase screen height.