We employ the recently developed multi-photon R-matrix method for molecular above-threshold photoionization to obtain second-order ionization amplitudes that govern the interference in RA-BITT experiments. This allows us to extract RABITT time delays that are in better agreement with non-perturbative time-dependent simulations of this process than the typically used combination of first-order (Wigner) delays and asymptotic corrections. We calculate molecular-frame as well as orientation-averaged RABITT delays for H2, N2, CO2, H2O and N2O and analyze the origin of various structures in the time delays including the effects of partial wave interference, shape resonances and orientation-averaging. Time-delays for B and C states of CO + 2 are strongly affected by absorption of the second (IR) photon in the ion. This effect corresponds to an additional contribution, τ coupl , to the asymptotic approximation for the RABITT delays τ ≈ τ mol + τcc + τ coupl . Applicability of the asymptotic theory depends on the target and IR photon energy but typically starts at approximately 30 -35 eV of XUV photon energy.