That... almost worked.
However, the resulting raster only has one band, which definitely doesn't work for me. Is there anyway to preserve the number of bands?
You may want to try the Copy Raster (data management) tool.
Sorry to take so long replying:
Using Copy Raster with the processing extent set had no effect whatsoever - the bounds are still a half pixel extra on each side.
This problem isn't crucial or time-sensitive - I have been able to project this dataset and display it as imagery with no troubles, other than dismissing the extent error in ArcMap.