The default method align_epi_anat.py uses is a full affine transformation with 12 parameters. You can override this with the -Allineate_opts option. This just passes those options along to 3dAllineate, so any valid 3dAllineate options can be used. Replace the "-warp aff" with the option you want.

From align_epi_anat.py's help:
-Allineate_opts '-ssss -sss' : options to use with 3dAllineate. Default
options are
"-weight_frac 1.0 -maxrot 6 -maxshf 10 -VERB -warp aff "

From 3dAllineate's help:
-warp xxx = Set the warp type to 'xxx', which is one of
shift_only *OR* sho = 3 parameters
shift_rotate *OR* shr = 6 parameters
shift_rotate_scale *OR* srs = 9 parameters
affine_general *OR* aff = 12 parameters
[Default = affine_general, which includes image]
[ shifts, rotations, scaling, and shearing]