Thanks to durron597 for the pointer to the related question which gave me enough to figure out.  The answer is to use a child injector to take action on the previous injectors output.  Example below:
Injector propInjector = Guice.createInjector(new PropertiesModule());
PropertiesService propService = propInjector.getInstance(PropertiesService.class);
Injector injector = propInjector.createChildInjector(new MyModule(Objects.firstNonNull(propService.getProperties(), new Properties())));
Injector is now your injector for the remainder of the app.
And then in MyModule you can take action on the created objects:
public class MyModule extends AbstractModule {
private final Properties properties;
public MyModule(Properties properties){
    this.properties=properties;
}
@Override
protected void configure() {
    // export all the properties as bindings
    Names.bindProperties(binder(), properties);
    // move on to bindings
    // bind(..);
}
}
In case it helps anyone else..!