I\'m getting System.IO.FileNotFoundException: The specified module could not be found
when running C# code that calls a C++/CLI assembly which in turn
The answer for the GUI, other than changing output settings, was the addition of a Pre-Build Step
copy $(ProjectDir)..\Debug\BackingStore.* $(TargetDir)
The answer for the Test projects was to add the missing DLL to the Deployment tab of the testrunconfig. You can either do so by directly editing the default LocalTestRun.testrunconfig (appears in Solution under Solution Items) or right-click the Solution and Add a new test run config, which will then appear under the main Test menu.
Thanks for the answers on this SO question on test configurations for leading me to the answer.