afni.nimh.nih.gov

I think you're right. It looks like AFNI_BYTEORDER will override the input dataset's byte order. If it is not set, then I think it takes the byte order from the input. Possible solutions are not to set AFNI_BYTEORDER or to set the byte order to the one you want. With some small changes, you could swap bytes or avoid AFNI_BYTEORDER completely in 3dcopy.