I was having the same problem and I called shopify to receive the same unsatisfactory answers. I just stumbled upon this solution in another forum thread and it at least allowed me to add a nice line right before the shipping options that says "Please allow 1-2 days of handling before the shipping estimates". I am thrilled to have found this solution.
Online Store> Themes> Actions> edit languages > cart > search "shipping method notice"
you can then insert your notice that will appear before the shipping selection
Hope this also provides a working solution for some of you!