The ionization of H-2 Rydberg states at a metal surface is investigated using a molecular beam incident at grazing incidence on a gold surface. The H-2 molecules, excited by stepwise two-color laser excitation, are selected in each of the accessible Stark eigenstates of the N+ = 2, n = 17 Rydberg manifold in turn and the ionization at the surface is characterized by applying a field to extract the ions formed. Profiles of extracted ion signal versus applied field show resonances that can be simulated by assuming an enhancement of surface ionization at fields corresponding to energy-level crossings between the populated N+ = 2 manifold and the near-degenerate N+ = 0 Stark manifolds. It is concluded that the slow (microsecond time scale) rotation-electronic energy transfer to N+ = 0 states occurring at these crossings takes place in the time interval following application of the field ramp when the molecule is still distant from, and unperturbed by, the surface. However, the energy levels are strongly perturbed by image-dipole interactions as the molecule approaches close to the surface, leading to additional energy-level crossings. Adiabatic behavior at such crossings affects the intensity of the observed resonances in the surface ionization signal but not their field positions. Resonances are also observed in the surface ionization profiles at fields above the field-ionization threshold; some of these show asymmetric "Fano-type" line shapes due to quantum interference in the nonradiative coupling to degenerate bound and continuum states.