Ok, so its based on that line of Poe, not that the Resistance got the intel. Ok, that clears up that part since that was a bit confusing.
I think the better solution if people or really hounding on needing the resistance hear something. Forget the goofy broadcast. Just have part of the conversation of the First Order in their board room. Put some radio affect on it and THAT is the intel they got. Essentially, Hux recorded the conversation and sent it, with out intel, to the Spy to relay. That way, the Resistance hears part of that recording, that the audience has heard, and the next scene is the Resistance all together.
This allows 1.) Show and not tell (just need a section of the “board room meeting” audio distorted to achieve this). and 2.) The good guys can still can be at a disbelief on what they’ve heard and keep the lines of “Can we believe this?” and “Somehow he is alive” if needed.
Win win.
(The fortnite lines are just too corny, sorry.)