I suggest to use EPSG:3857
as CRS for the raster during the tiling process.
EPSG:900913 is not included in current GDAL and QGIS anymore, thus the special spherical mercator treatment is not applied. The proj definition for EPSG:3857 is
+proj=merc +a=6378137 +b=6378137 +lat_ts=0.0 +lon_0=0.0 +x_0=0.0 +y_0=0 +k=1.0 +units=m +nadgrids=@null +wktext +no_defs
which is a bit contradictional to
SPHEROID["WGS 84",6378137,298.257223563,AUTHORITY["EPSG","7030"]]
typically causing the offset of 20 to 30 km to the North.