Looks like mosaic.tif is compressed while smoothing.tif is not:
Image Structure Metadata: COMPRESSION=LZW
I don't have any experience with orfeo, but it seems you can pass GDAL creation options to create compressed outputs by using an "extended filename", see:
Georeference by coordinates in polygon units rather than geographic. That is, (0,0) for the polygon in the bottom left corner, etc. You'll need a lot of points and a non linear transform function, which is available in QGIS.
Then take the value of each polygon as z and its x,y coordinate as an x,y,z ungridded dataset.
Grid the x,y,z data to a raster and ...