Hi,
Generally for this type of deep integration, the recommended solution is build a custom integration app for your store and HawthroneGC and host this on some cloud service yourself. The do-it-yourself approach can certainly work, but will incur pretty expensive cost to maintain it long term.
We offer an integration platform called Shypyard (https://apps.shopify.com/shypyard) to connect Shopify stores with third party services, and your use case is quite perfect for us. In your case,
1. what you will need is one directional integration that looks for product create/update on HawthroneGC, and create/update them on Shpoify's end. We can customize on what product properties to be synced to Shopify after the initial creation so that you are free to update certain properties like pricing on Shopify.
2. Integration from Shopify order to HawthroneGC. This can be a bit trickier as there are more integrations that you may want (i.e. order update, order cancel, shipment/fulfilment status update, etc)
This is assuming those API endpoints are actually possible with Hawthrone. Taking a quick look at the API doc you shared, it isn't obvious if order creation via API is possible. In this case, we will need to explore other alternatives like potentially generating a csv of orders that can be imported to Hawthrone's admin interface (assuming this is supported).
