Hello,
You could use Shopify API for your all stores which will be managed by a small apps I will write for you as an intermediate layer apps. This apps will interact with your local system over its SDK, in case it has it. Otherwise, let me know. So, I could integrate with my apps.
Using my method, it can be set as 2 ways sync in certain durations/intervals, e.g.: per 5 minutes or quicker.
Let me know your feedback
Regards,
Khamid