A bit odd that a challenge so easy could be solved so simply. There were many, many layers of nested ZIP files, RAR files, and TGZ files. Inside each was a folder called work_folder containing the next archive.

A one-line bash script was enough to extract it fully using the wonderful 7zip (after the initial archive is renamed to 100):

for archive_number in {100..1}; do 7z x $archive_number; 7z x $archive_number~; cd work_folder; done