Building upon the hybrid strong/weak coupling model for jet quenching, we incorporate the effects of transverse momentum broadening and contributions from the response of the plasma to the jet, aka the wake, and study their effects on a variety of observables. We find little sensitivity to the strength of broadening for inclusive observables. However, we propose new observables constructed from ratios of differential jet shapes, in which particles are binned in momentum, which are sensitive to the value of the in-medium broadening parameter. We also study dijet and boson-jet acoplanarities and find a generic narrowing of the angular distribution with respect to the vacuum due to energy loss. Finally, we investigate the effect of the backreaction of the medium on the angular structure of jets as reconstructed. We provide a detailed analysis of the so called "missing-pt", finding a qualitative agreement between our model calculations and data in many respects, as well as evidence that our simplified analysis of the hadrons originating from the wake in the plasma underproduces semihard particles.