Hey Jeff,
You should be able to skip step 2 and have the app get notified when new orders come in using webhooks.
You could use an app like Zapier (I'm NOT affiliated with this app) and skip having to touch the Shopify API (Create a Trigger for New Paid Order and use the GET Action to send data to your app).
If that doesn't work for you, get in touch and I'll be happy to help you out with this: http://experts.shopify.com/simpthings