The contrast in the EPI dataset doesn't have bright CSF relative to the tissue, and the default alignment relies on that. However, the alignment works well with lpa or nmi cost functions instead of the default for anat to epi alignment cost function of lpc or lpc+ZZ.
align_epi_anat.py -cost lpa -multi_cost nmi -anat anat_strip+orig. -dset2_strip None -epi rest_am+orig. -epi_base 0 -dset1_strip None -suffix _al2epi2 -deoblique off -overwrite