Large-scale laboratory experiments were performed on the Coriolis rotating platform to study the stability of intense vortices in a thin stratified layer. A linear salt stratification was set in the upper layer on top of a thick barotropic layer, and a cylinder was towed in the upper layer to produce shallow cyclones and anticyclones of similar size and intensity. We focus our investigations on submesoscale eddies, where the radius is smaller than the baroclinic deformation radius. Towing speed, cylinder size and stratification were changed in order to cover a large range of the parameter space, staying in a relatively high horizontal Reynolds number (Re = 2000-7000). The Rayleigh criterion states that inertial instabilities should strongly destabilize intense anticyclonic eddies if the vorticity in the vortex core is negative enough zeta(0)/f < -1, where zeta(0) is the relative vorticity in the core of the vortex, and f is the Coriolis parameter. However, we found that some anticyclones remain stable even for very intense negative vorticity values, up to zeta(0)/f = -3.5, when the Burger number is large enough. This is in agreement with the linear stability analysis performed in part 1 (J. Fluid Mech., vol. 732, 2013, pp. 457-484), which shows that the combined effect of a strong stratification and a moderate vertical dissipation may stabilize even very intense anticyclones, and the unstable eddies we found were located close to the marginal stability limit. Hence, these experimental results agree well with the simple stability diagram proposed in the Rossby, Burger and Ekman parameter space for inertial destabilization of viscous anticyclones within a shallow and stratified layer.