The issue is that if the shipping settings are too complex, albeit it might be simple to you, the google and youtube app will not be able to match the shipping settings.
The second problem is that because you are using this app, you will not be able to setup shipping settings manually.
Your second problem is that custom products are not really supported in Google Shopping, and as such, not knowing the product weight is not an outcome supported by Google, unless you specify a specific shipping rate.
So one, I want to caution you for submitting products that are not finished, as Google expects goods to be in it’s finished form before listing it on the website. However there are situations you can keep some products not in stock, if for example you keep the most popular products / variations in stock, and the not so popular products not in stock, as explained here: https://support.google.com/merchants/answer/7162856?hl=en
Now for the shipping issue, that you can’t edit, I recommend you use the following app for your data feed: https://apps.shopify.com/multiple-google-shopping-feeds
Then you can setup a fixed shipping rate, that is equal or greater then what you charge in the checkout.