I have found a workaround for my problem. Rather than picking all the relevant folders and files one by one with the ContentChooser, I put them into a zip archive. Thus, I can import the whole structure into the DirInternals in a single go by unzipping from wherever they might come (another app, download, by usb file transfer etc.). The relevant MIME for the CC is "application/zip/*"
By the way: the zipped file must first be copied to DirInternals before the archiver is called to unzip. The archiver cannot handle the CC result.