Tiggywiggler (19/08/2016)
You can replace the EstimateShipping control with the code from the download so that it is replaced, however, the original problem will still remain.
I'd like to bring you up to speed. Thanks to the advice from Paul (Kartris), I recreated the database, and many issues resolved.
The shipping issue (both at estimate in the basket, and at the choice list in checkout) are still ongoing. I wonder if you can help me reverse your modifications (I will download a backup of your work before any reversing), to see if this was also resolved.
Can you confirm where you made your changes? Was it "ShippingMethodsDropdown" or "ShippingMethodsEstimate"?