If you don't use Shopify for your order management:
Within your inventory management software/provider, there should be some way to "categorize" or "tag" the entire "Carbon Neutral Order" product as non-inventory so that the entire order can pass through without having to be manually advanced. Sometimes this is referred to as “blacklisting” or “whitelisting” a certain product.
It would be helpful to ask your inventory management company how they would handle gift cards. This is similar to a gift card in that it's not “physical” and therefore doesn't need to be fulfilled, but can't prevent the entire order from being fulfilled. It's a product that you need to sell on your site, but that doesn't require any shipping or fulfillment (just like a gift card).
That is how our other merchants have successfully solved this issue.
Additionally, we have a feature that allows you to define the SKU name for each variant that gets created. You can find this in the Customization Settings of your EcoCart Dashboard.
If you do use Shopify for your order management:
For fulfilling orders at the Shopify level, that should be happening by default with EcoCart if you have the newest version. You will see an option in your EcoCart Dashboard for automatically fulfilling the “Carbon Neutral Order” product. Make sure the box is checked if you’d like the product to be automatically fulfilled.
If the box is checked and it’s still not being automatically fulfilled properly, you may not be working with the most updated version of EcoCart. If that’s the case, all you have to do is uninstall, then reinstall the EcoCart Shopify app. Then all your orders from there on out with the EcoCart product should no longer come as “partially fulfilled” or “unfulfilled.”