This is how I resolved the problem of "No Shipping Method Found"
I am using the non-purchased (i.e. free) version of HikaShop. This means I am limited to one registration type, requiring all purchasers to create an account. That's not a real problem.
From the back end, System > Configuration, I modified the Checkout workflow in the upper left. At the very bottom of the Checkout workflow section is a link to "Add Step." This allows the administrator to add another page. Therefore My checkout workflow now has five different pages and looks something like this:
[Cart]
[Address] [Login]
[Cart] [Shipping]
[Coupon]
[Cart] [Payment]
Now, when a customer goes to checkout, they first see a summary of what's in their cart, and a [Next] button.
When they click next, the page refreshes and asks them to login (if using the paid version and selecting No Registration option in back end, the user is given an address pop-up).
Once logged in (in my case) the address data is displayed for verification, along with a [Next] button.
On the next screen, the USPS shipping method is displayed as expected, with no errors along with the cart summary and a [Next] button.
Then ask for coupons
Then summarize the cart one more time and have the user submit payment.
So, I got what I needed for the version of the HikaShop product I'm using. No error message and the workflow operates as I would expect it to.
HikaShop for the WIN! (despite my earlier comment about the deal breaker... turns out HikaShop has a way to do what I wanted it to do).
Hopefully this procedure will help others.