You're both forgetting that first, we were shown a graphic of the seeding pattern the Progenitors used, a spiral moving across the galaxy, and across the Alpha and Beta quadrants. Once again, it may have touched the Gamma and/or Delta quadrants, but only just. And that spiral pattern, once it was figured out, led our heroes to every last world that had been seeded that had not yet been found. Every last one, which was needed to find the entire message.
If the Progenitors left their seeds anywhere else in the galaxy, it was part of a separate spiral, and had a separate message. It may have been the same message as far as wording or their hope for peaceful co-existence, but it wasn't the message they left for our heroes to find. This, actually, is my head-canon for why so many Delta and Gamma Quadrant species have the same hominid appearance that we're so familiar with in the Alpha and Beta Quadrants. There was more than one group of Progenitors, and each one had the seeds, and the message that they wanted to pass on. But each group acted on their own, and spread the seeds where they chose, not as part of a master plan.
