GPS data is added only when shooting via the app as the mobile device is providing the data.
Hmm, this is strange … Did you try to narrow down which EXIF tag actually made this possible?
From you comparison of the EXIF tags, I see nothing suspicious.
No, not without the flaws you also noticed in the result of the Ricoh stitcher.
Without any further input, PTGui uses some default for the lens correction and alignment parameters which may not suitable for your camera. In case you have no camera-specific template with the correct parameters, you can usually use automatic control point generation. But surprisingly, this fails for this image. PTGui seems to be confused by the image. Maybe this is caused by the reflections on the mirror and shiny surfaces.
Therefore, I added some control points manually. This eliminated the rough stitching errors but some flaws still remain (see the tiles over the bathtub):
