Resolved by essentially removing the docker/app folder, thus forcing invoice ninja to reinitialise it. The steps were as follows:
# Remove the docker/app folder
sudo rm -rf docker/app
# Restore the .keep files
git checkout docker/app
# Restore permissions
chmod 755 docker/app/public
sudo chown -R 1500:1500 docker/app
# Now start the container
sudo docker-compose up -d
The app is now up and running again!
I did want to check one thing before I delete the backup - is there anything user-specific in the app folder that I would need to restore?