So changing the acquisition direction seems to orient the images properly:
Per-frame Functional Groups Sequence (5200,9230)
>Plane Position Sequence (0020,9113)
>>Image Position (Patient) (0020,0032) = -96.313\-89.5543\-73.0048
>Plane Orientation Sequence (0020,9116)
>>Image Orientation (Patient) (0020,0037) = 1\0\0\0\1\0
>Pixel Measures Sequence (0028,9110)
>>Slice Thickness (0018,0050) = 2
>>Spacing Between Slices (0018,0088) = 2
>>Pixel Spacing (0028,0030) = 2.01923\2.01923
:
:
>Plane Position Sequence (0020,9113)
>>Image Position (Patient) (0020,0032) = -96.313\-89.5543\-71.0048
>Plane Orientation Sequence (0020,9116)
>>Image Orientation (Patient) (0020,0037) = 1\0\0\0\1\0
>Pixel Measures Sequence (0028,9110)
>>Slice Thickness (0018,0050) = 2
>>Spacing Between Slices (0018,0088) = 2
>>Pixel Spacing (0028,0030) = 2.01923\2.01923
:
:
Results in a correct BRIK.
However, if the images are ordered S -> I, the result is an upside down brain with incorrect DICOM coordinates. It appears AFNI is using the origin point from the first item in the Per-frame Functional Groups Sequence and assuming it is the most inferior slice (axially). This may be a serious issue for enhanced MR images collected sagittally.
I was able to correct using
3drefit -orient RAS raw+orig
