Reading this thread again led me to the solution, thank you for fixing this in Version 1.6.5, just tried it.
Of course there are many other options neglected in .xml for Export Orthomosaic settings e.g. JPEG compression value, Generate Tiff Overview, Write alpha channel, etc.
The reported issues with Compression, Region and no-data sections should be fixed in the 1.6.5 version update.
We were missing the BigTIFF parameter in the batch xml. It does not get saved in any way and is not read in again.
I correctly guessed it should be something like tiff_big, and finally these parameters appeared:
<image_compression>
<tiff_big>false</tiff_big>
<tiff_tiled>false</tiff_tiled>
<tiff_overviews>false</tiff_overviews>
<tiff_compression>5</tiff_compression>
<jpeg_quality>90</jpeg_quality>
</image_compression>
None of the image_compression options seemed ever to get saved or read in before v. 1.6.5.
Now they do!
To use it in a python based workflow see
https://www.agisoft.com/forum/index.php?topic=11687.msg52407#msg52407compression = Metashape.ImageCompression()
compression.tiff_big = True
chunk.exportRaster(path = "path/to/file.tif", source_data=Metashape.OrthomosaicData, image_compression = compression)