Dispersive shock waves in thermal optical media are nonlinear phenomena whose intrinsic irreversibility is described by time asymmetric quantum mechanics. Recent studies demonstrated that the nonlocal wave breaking evolves in an exponentially decaying dynamics ruled by the reversed harmonic oscillator, namely, the simplest irreversible quantum system in the rigged Hilbert spaces. The generalization of this theory to more complex scenarios is still an open question. In this work, we use a thermal third-order medium with an unprecedented giant Kerr coefficient, the m-cresol/nylon mixed solution, to access an extremely nonlinear, highly nonlocal regime and realize anisotropic shock waves with internal gaps. We compare our experimental observations to results obtained under similar conditions but in hemoglobin solutions from human red blood cells, and found that the gap formation strongly depends on the nonlinearity strength. We prove that a superposition of Gamow vectors in an ad hoc rigged Hilbert space, that is, a tensorial product between the reversed and the standard harmonic oscillators spaces, describes the beam propagation beyond the shock point. The anisotropy turns out from the interaction of trapping and antitrapping potentials. Our work furnishes the description of novel intriguing shock phenomena mediated by extreme nonlinearities.