Running 1 set of tests on different versions of 1 tested app

I have a test project, and I want to use the same set of tests on different versions of the same application. For instance, Application A has a version 1 and a version 2. The tests focus on the GUI functionality of Application A. And there are no GUI changes from v1 to v2. I want to be able to use the same test project on both versions.

To simpify things:

I created a keyword test with TestComplete automatically mapping objects. I added each version of Application A on the TestedApps screen. My keyword test is originally recorded using v1 of Application A. I am now trying to get this test to run for v2 by calling 'run testedapp' and setting it to run v2. This doesn't work. And I need help to make it run.

For more info:

On the NameMapping screen I created two configurations, one for each version. For each configuration, I changed the 'FileVersionInfo' and 'Path' properties of the Application A mapped object.  I also added a 'run code snippet' action to run NameMapping.CurrentConfigurationName to the test (this action is called first in the test). This will activate the Name Mapping Config for the version I want to run (in this case, the config for v2).

Other than the name mapping, I have read on the Smartbear Support site how to use variables. But since I am using the NameMapping and TestedApp feature, I don't know if I will need to set a global variable/constant further identifying the two versions.

I know I am missing something, but I don't know what.  I am using TestComplete v8.70.727.7, and Application A is a 64bit program.