You can accomplish what you're describing using Intuitive Shipping. I am wondering if you are open to offering freight rates directly at checkout since this is also an option with the app. This way, customers are more likely to convert since they will know the shipping cost upfront. It also saves you time (time=money) from having to manually calculate the freight costs.
I encourage you to book a demo with our team who can give you a tour and show you how Intuitive Shipping can give you the exact results you want at checkout, including the messaging you want.