To pull and put the data, you will need to add all of this directly to the database, rather than trying to import it all.
I have worked with WooCommerce for a long time, and can get all orders, user data, order information, and all gravity forms entries added to your new site within 1 day.
And the Github item you put up won't help with the data move, because it uses the same idea as the All Import function does on WP, which is using PHP, and this is what will be timing out on your hosting server
Please message so we can discuss further,
Daniel Larson