I set up local test site using zen 1.37 and the latest GCO 1.0.5 and observed the following using table rates.

CASE 1: I place an item in the cart, go in the cart, press the GCO button which takes me to GC site. Shipping and Tax are correct. Note, I didn't log in as a customer.

CASE 2: Now, I place an item in the cart, go in the cart, press the Go Checkout button which takes me to the Login Page. I press the GCO button which takes me to GC site. Tax is correct but Shipping is $0.00 !

From your description of your issue, were you doing the steps described in Case 2 above?