We report an experimental study addressing the characteristic hydrodynamic transformations of unstable wave groups as well as JONSWAP wave fields propagating from deep-water towards shallow regions. Long zones of linearly rising floor levels have been installed to mimic a simplified coastal morphology. The breather surface elevation evolution data show a very good agreement with the depth-adapted nonlinear Schrödinger-type model. Our results suggest that the residual effects of four-wave resonance interactions in the shallower regions is relevant for the nonlinear group propagation over steep bottom topography slopes. When considering broadband JONSWAP processes, the model fails in predicting the evolution of kurtosis, independently of the values of significant wave height adopted. Nonetheless, consistency with the data is achieved when narrowing the spectrum of the JONSWAP wave field. Our study emphasizes the strong potential of weakly nonlinear frameworks in modeling complex wave shoaling problems and wave transformations in coastal zones.