  Recent observations reveal that spectral breaks at ~GeV are commonly present
in Galactic gamma-ray supernova remnants (SNRs) interacting with molecular
clouds and that most of them have a spectral ($E^2dF/dE$) "platform" extended
from the break to lower energies. In paper I (Li & Chen 2010), we developed an
accumulative diffusion model by considering an accumulation of the diffusive
protons escaping from the shock front throughout the history of the SNR
expansion. In this paper, we improve the model by incorporating finite-volume
of MCs, demonstrate the model dependence on particle diffusion parameters and
cloud size, and apply it to nine interacting SNRs (W28, W41, W44, W49B, W51C,
Cygnus Loop, IC443, CTB 37A, and G349.7+0.2). This refined model naturally
explains the GeV spectral breaks and, especially, the "platform"s, together
with available TeV data. We find that the index of the diffusion coeffcient
\delta\ is in the range of 0.5-0.7, similar to the galactic averaged value, and
the diffusion coefficient for cosmic rays around the SNRs is essentially two
orders of magnitude lower than the Galactic average, which is a good indication
for the suppression of cosmic ray diffusion near SNRs.
