I haven't seen the gantry tilt before, but someone had dealt with the DICOM files in Matlab.

[www.mathworks.com]
[www.mathworks.com]

I tried a couple things in AFNI that might be right (but they might be wrong too).

3dWarp -deoblique -prefix ct_rot_deob ANATOMIC-NO_GROUP-CT-3-2+orig.
3dcopy ct_rot_deob+orig. ct_rot_deob_fix3
3drefit -ydel `ccalc 'tand(30)*0.5` ct_rot_deob_fix3+orig.

The result looks roughly right, but it's hard to know for sure. The standard DICOM parameters you mentioned do contain the 30 degree information, but it needed a bit more attention to handle an additional shearing and not just a rotation. Here I deobliqued the data by tilting the data back from its 30 degrees and then adjusted the voxel size in the y-dimension to compensate for the distortion. You may want to align this to an MRI structural image. Since this image is mostly skull, you might try aligning to just the skull image in the MRI possibly using 3dSkullStrip and 3dcalc and then align_epi_anat.py.