It's been a year to the original question, so not sure if you're still looking for an answer to this. Yet..
From your description, it seems like you want to build a web app that manages multiple WooCommerce stores from a single interface.
I saw a video demo of such a solution a few weeks ago. It's called Multishop - https://multishop.io/
There is also a proposed fork to WooCommerce to support multiple sites - http://woomu.org/
And here's a similar idea on WooCommerce Ideas board - http://ideas.woothemes.com/forums/133476-woocommerce/suggestions/4295981-multiple-shops-one-backend
We build some popular WooCommerce extensions. One of our plugins - Smart Manager - lets people manage products, inventory, orders and customers easily. Smart Reporter does advanced reporting on WooCommerce.
We have also looked at WC API and upcoming WP API.
It's great that you've setup WC multisite on your own. But if you don't like PHP, and want to rely on WC / WP APIs, I believe this is going to be a difficult project.
In all likelihood you'd need your own plugin. WC / WP APIs may not be sufficient for your needs. Another challenge is maintaining compatibility with ever growing list of WC extensions. So if you plan to build the web app for anyone (rather than a set of WC installs you control), you will need to invest significant energy in managing compatibility and updates.
And if the reason you wanted to build your app was to provide a simpler UI / UX, you can still build a plugin that hides all complexities. Or contribute to WooCommerce core with your suggestions / ideas / patches.