I am working on a flower wholesaler Shopify store and I am facing a problem with my shipping rates.
I added a calendar on my cart page that let customers choose delivery date and time (2 hours time slots); once the desired date and time have been selected I would like to charge different rates according to the time chosen in a way that on the checkout page the customer sees only the shipping rate that is assigned to the desired delivery slot.
In my experience, Zapiet was the best solution for this sort of situation. They're a good crew of support staff, and it sounds like what you need is exactly what they're set up for. Hope this helps!