Combining overviews for a large multiband raster image?

The .ovr overview is a multipage TIFF, consisting of successively coarser images. For the overview of a multiband image (as produced by gdaladdo) each of those pages is itself a multiband image.

In principle it should be possible to:

1. Split the pages, from each band's overview, into separate files (almost by streaming i.e. without decompressing the image data),
2. Collate those pages by resolution (e.g. build a multiband vrt for each zoom factor)
3. Re-encode the image data, as a multiband TIFF image for each zoom factor. (Only at this step the image data may need to be decompressed and recompressed, to facilitate the reorganisation.)
4. Gather the multiband series together as pages of a single file.

A complication is that Libtiff utilities don't have great support for GDAL extensions (such as the nodata value tag); ImageMagick utilities (e.g. convert) have a tendency to always (prematurely) decompress the data into an image in memory.

As for GDAL utilities: gdaladdo accepts a COPY_SRC_OVERVIEWS option, but still seems inexplicably slow. May be able to copy a page by referring to it as GTIFF_DIR:<page$>:<filename>?