A is a module project. There are some test targets and the relevant reusable code is compiled in a separate (static library) target. A uses the third party Lumberjack logging library. The Lumberjack code was simply dropped into the project.
B is a different module project, but otherwise it has the same properties as A.
C is the main project. It depends on A and B. It links the libraries of A and B.
Compiling C will result in duplicate Lumberjack symbols.
How can I have multiple separate module projects so that...
Since you are targeting OSX, the solution to your issue is building Lumberjack as a framework (as opposed to link the sources code in your A and B modules) and then using that framework wherever it is required (i.e., in any project using A or B modules).
Indeed, Lumberjack already includes a project that will build a Lumberjack.framework, check this: CocoaLumberjack/Xcode/LumberjackFramework/Desktop/Lumberjack.xcodeproj.
Elaborating more on this, you would define your A and B modules as you are doing now, but without dropping Lumberjack source code in it. What you do instead is, whenever you want to use the A static library in a executable (say, your test target), you add the library to the target and also the lumberjack framework (exactly as you do with OSX SDK frameworks).
Adding the dynamic framework is just a different way to "drop the sources", if you want, but done properly.
When you want to use both A and B in a C project, you add both static libraries and your Lumberjack framework to C.
As you can see, this way of doing will comply with all your four requirements, at the expense of introducing one dependency: you need to make clear in your static libraries documentation that they depend on the Lumberjack framework. This is actually not a big issue, since the latter is available in its own project and any one will be able to build it on his own.
If you want to improve on the handling of this dependencies, cocoapods are the way to go (a cocoapod is a file associated to your library which describes its dependencies, so when you install your library, the cocoapods system will automatically install also the dependencies). But this is highly optional. One single dependency is not a big issue to document or comply with.
Hope this answers your question.