I would carefully read my comments here and here. Modern versions of dcm2niix should correctly extract slice timing for most GE and Siemens scanners, so I assume your data is from a Philips system. You also suggest you are confident that the slice acquisition is sequential, not interleaved. I strongly recommend you contact the Philips scientist who is associated with your center to ensure correct details (these individuals are Research Collaboration Managers in Siemens-speak, but I believe they are 'Clinical Scientists` for Philips users).
I would use a tool like fslhd to determine the order of slices on disk. For example:
fslhd fmri.nii
...
sform_xorient Left-to-Right
sform_yorient Posterior-to-Anterior
sform_zorient Inferior-to-Superior
This reports how columns (x), rows (y) and slices (z) are stored on disk. In this case, the slices are stored in the order inferior to superior, so the first slice on disk is the most inferior. I have never seen dcm2niix convert data from any vendor in the Superior-to-Inferior.