Yeah. I'm in the same place, unfortunately.
It's apparently a pretty common problem, too. The usual solution offered around here is to contact the USPS Web Tools people and ask them to switch your Web Tools account from testing to production mode, as outlined by Dougadanny here. That will probably work for you, so it's totally worth trying.
On the other hand, I know my USPS Web Tools account is already in production mode because I've been using it with OpenCart for three years. But I've been getting exactly the same error from PrestaShop that you have! And there seem to be a few other folks for whom that solution didn't work, too.
So another option—one I'm definitely looking into—would be trying a different module for USPS integration. People seem to like this one, for example.
Best of luck!