Shopify App's Custom Shipping Model

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I'm working on an app, which has a custom(a bit unusual) shipping model. Let's establish the involved entities first;
  1.  Shopify
  2.  Shopify Store (has it's own location and address)
  3.  Shopify Customer (has it's own location and address)
  4.  Shopify Partner App (has it's own location and address)
The app intends to provide to recycling services to the customers. For this purpose, the app gets installed to a store and then the app adds it's Product(lets call it product X) to the store.
Now, customers willing to get their material recycled will add that product X to their cart and place an order(the order can have other products from the store).
Here's the complicated part, how can the package be shipped from Customer to Shopify App Owner's address  so that it can be recycled?
Is there something which Shopify can provide to deal with such scenarios? I came across the concept of Return Shipping Labels(but not sure how they work and to what address they will be intended to be returned to).
Moreover, if we manage to pull this off, then after that how to include these shipping charges in the invoice for the customer(as this is not the normal flow and Shopify usually calculates shipping from Store's location to the Customer's shipping address) ?
My Shopify App can identify the orders containing its product X, and can extract the Shopify Customer's Shipping address(to do some processing, if needed). The Shopify Customer has to send the recycle-able material package to the Shopify Partner App's address.
I know that it's not how Shopify usually works with shipping , but I need to get the possibilities listed down for my use case.

Thank you for your time,
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