After enormous amounts of frustration, I've finally worked out a recipe for working with composer, git and deployHQ - the submodules were the fly in the ointment, here is how to work with them.
First, create a new Drupal project using composer
>$ composer create-project drupal-composer/drupal-project:8.x-dev my_site_name_dir --stability dev --no-interaction
Next, rename web to public_html - so it plays nicely with cPanel
edit composer.json file - swap this in to replace the extras section renaming web to public_html