You can directly modify the test target in your Example project to include the private headers in the Header Search Paths. Just go into your Unit Test target, and under Search Paths -> Header Search Paths, add:
$(inherited) "${PODS_ROOT}/Headers/Private/Example"
In your unit test files, you can include the headers like so:
#import "PrivateHeaderForComponent1.h"
#import "PrivateHeaderForComponent2.h"
rather than the typical #import <Example/PrivateHeaderForComponent1.h>
The downside is you're making assumptions about how CocoaPods lays out the files in the Pods directory, but I would rather do that than change my public podspec file.