It is experimentally demonstrated that (electron plus exciton) core-excited resonances are formed by low-energy electron scattering in the Ar, Kr, and Xe rare-gas solids at 11.6+/-0.2, 9.7+/-0.2, and 7.7+/-0.2 eV, respectively. These resonance states can be efficiently coupled with dissociative Rydberg anion states of adsorbed H2O, C2D6, and C6D6, but not with valence-dissociative states of adsorbed O2 or C6D6. These resonances are revealed as narrow (full width at half maximum DELTAE = 0.2-0.4 eV) enhancements in the dissociative attachment yields of the adsorbed molecular species, at incident electron energies just below that of exciton formation in the condensed rare gases. Above the exciton energies, in contrast, the dissociative attachment mechanism in the adsorbed molecules can be attenuated, or completely quenched. All observations are characterized as ''quasi-two-electron-jump'' processes due to sizable overlaps between the associated Rydberg orbitals.