Display ALL available ship methods during checkout

I have a B2C storefront that gets a lot of activity. Through user study we have noticed that an exceptionally high percentage of customers will blow through the checkout process without even realizing they have choices when it comes to shipping cost. Why, because in the cart, the ship method is buried in a drop-down list. Think of other big ecommerce sites you shop on - amazon, target, walmart, the billions of shopify sites - during checkout you see all of the shipping methods and rates at once, without having to click on anything, and you can easily just select the one you want.

I would like Pressero to consider moving the ship methods from a drop-down list to a datagrid of some sort, so that the customer can easily see all shipping methods and rates available to them.

We are getting accused of trying to make more money from the customer by not offering a choice of shipping rates because the least expensive shipping rate does not always show up first in your drop-down list, and they didn't realize until afterwards that they had a choice. And now that creates friction with the customer, extra time on my end apologizing to the customer and then having to issue a refund. This happens more than you might realize and it can be easily fixed by changing the way you display the shipping methods during checkout.