Recent works have shown that the spectroscopic access to highly excited states provides enough information to characterize transition states in isomerization reactions. Here, we show that information about the transition state of the bond-breaking HCN-HNC isomerization reaction can also be achieved with the two-dimensional limit of the algebraic vibron model. We describe the system's bending vibration with the algebraic Hamiltonian and use its classical limit to characterize the transition state. Using either the coherent state formalism or a recently proposed approach by Baraban et al. [Science 2015, 350, 1338-1342], we obtain an accurate description of the isomerization transition state. In addition, we show that the energy-level dynamics and the transition state wave function structure indicate that the spectrum in the vicinity of the isomerization saddle point can be understood in terms of the formalism for excited-state quantum phase transitions.