Hello everyone!
Thanks for the super helpful discussion. I think I understand what is needed now to have two broadcast listeners that are guaranteed to hear all the broadcasts of a given other module. The moral of the story here is that I need to be careful and considerate of how these modules are being launched and in what order to ensure that the two listener modules in question are registered before sending confirmation back to the module doing the broadcasting. I also really like the "forwarding" approach suggested by Taggart. That seems like a useful way to ensure your target modules have what they need before everything else starts going.
Thanks again for your help everyone!
-John