Send Orders to Shopify Using My Own Custom Landing Page

Shopify Partner
1 0 0

I'm looking for a solution that will allow us to take orders using our custom hand coded landing page and then pass the order data to our shopify store, just like this app does for Clickfunnels users 

Tried Clickfunnels but it's too limiting in terms of being able to integrate an advanced custom landing page design that displays and functions as it should when we use our own server and traditional PHP driven coding. So I'm looking for something that can just push my order details into Shopify. 
I don't mind using any 3rd party order management system if they already have this capability to push the orders to shopify. I just need the easiest way to make this happen. Below is an example of the type of advanced 2 step landing pages we need to use this for. (Landing page with shipping details form) (2nd page checkout with product selection and billing details)