Peter and I took a quick look at the data, and I think we found a good solution. The EPI data has very little anatomical structure, in that CSF is not very visible as a separate bright intensity, so cost functions that rely mostly on the inverse relationship between bright intensity in EPI and low intensity in anatomical datasets don't work well. The solution is a different cost function, of course. I usually try lpa+ZZ and/or nmi to get at least a rough alignment. Here, this worked well. The anatSS.nii.gz dataset isn't skullstripped as well as I would hope, but it's good enough for this affine transformation.

align_epi_anat.py -anat anatSS.nii.gz -epi myEPI.nii.gz -dset1_strip None -dset2_strip 3dAutomask -cost lpa+ZZ -suffix _test1 -epi_base 0