Linear transforms can be applied to a volume without modifying the voxel data. If you use a 2D image viewer then most likely there will be no visible difference other than image orientation indicators (A/P, L/R, I/S).
Slicer creates a new series with only essential metadata.
If you want to “fix” a DICOM series keeping all data intact then it is a complex task, as you need to recompute image position and orientation tags and at least regenerate UIDs (series instance UID, SOP instance UIDs) for each DICOM file. If you are not sure how to do this then you can either try to find other software that would do such thing or use Slicer and accept that only essential fields will be set in the new series.
At this point, I would have been satisfied with just mirroring the images without fixing actual patient or image orientation tags in DICOM, but I can’t seem to be able to apply that simple transform to exported DICOM images.
So, if I were to recompute the tags (0020,0032)Image Position (Patient) and (0020,0037)Image Orientation (Patient), could you point me to a resource on how to approach this?