Hi - Thanks for pointing out the Biomedisa extension - It was discussed here a while ago, but really appears to have progressed a lot.
I didn’t watch the video you linked, but if you apply the same transform to the volume and the segmentation and then harden them, you should be able to save and restore them to nrrd and seg.nrrd file and have them reload in Slicer with the correct overlay because the headers will specify the correct orientation. If you need to change the pixel data you need to use something like the BRAINS Resample module.