Searching for any recent work on the DirecWay XML-RPC problem I came across a WordPress post. When I looked into the problem last spring, however, the problem seems to be with DirecWay's Web Acceleration product. Reboot the modem (thereby killing the accelerator) and XML-RPC calls work fine. Wait for the accelerator service to start and the XML-RPC calls fail regularly.
Maybe someday in the future DirecWay will fix this problem with their service. Or maybe someday rural customers won't be held hostage by this truly poor service provider.