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Visually correcting systematic shift between two geodatasets using QGIS

The equivalent question has been asked wrt ARCMAP, but I'm using QGIS and am also an inexperienced user.

I have multiple rasters, provided as geotiffs, that are all projected to the same custom CRS but are often offset by a few meters. I would like to treat one of them as correct and adjust the other rasters to match visually. A translation (shift by x/y) is all that's needed.

Is there a simple WYSIWYG-approach using QGIS to manually/visually translate one raster relative to its CRS or relative to another raster (and its CRS)?

It would be possible to georeference the rasters again, but they are quite close already, and I'm concerned about introducing errors of rotation and scale by doing that. I also don't know yet how to do that. I'm searching first for an answer that starts from the current, very close georeferencing solution.

If a WYSIWYG-approach doesn't exist, I could repeatedly guess at the translations necessary if I could modify the coordinates listed under Extent on the Information page of the raster's property sheet. Is that possible in QGIS?

Failing that, is there a way to translate the images using gdal command line utilities or python using gdal?

The answer for the ARCGIS version of this question mentioned a solution using a datum shift and another approach for raster data using ARCGIS' georeferencing toolbar. I haven't found equivalent functionality in QGIS yet.