That's not how I take what Rhaegar says. I think he did think Aegon was the fulfillment of the prophecy, and when he was trying for one more child/dragon head, he was hoping for Visenya since he already had Rhaenys.
The full House of the Undying vision says: (A Clash of Kings Paperback - Page 701)
Viserys, was her first thought the next time she paused, but a second glance told her otherwise. The man had her brother's hair, but he was taller, and his eyes were a dark indigo rather than lilac. "Aegon," he said to a woman nursing a newborn babe in a great wooden bed. "What better name for a king?" "Will you make a song for him?" the woman asked. "He has a song," the man replied. "He is the prince that was promised, and his is the song of ice and fire." He looked up when he said it and his eyes met Dany's, and it seemed as if he saw her standing there beyond the door. "There must be one more," he said, though whether he was speaking to her or the woman in the bed she could not say. "The dragon has three heads." He went to the window seat, picked up a harp, and ran his fingers lightly over its silvery strings. Sweet sadness filled the room as man and wife and babe faded like the morning mist, only the music lingering behind to speed her on her way
I like where you are going that Aegon could be meant to sit the Iron Throne, and someone else could be AA reborn or the Prince that was Promised so he has some purpose in the series, but I think Rhaegar thought he was the one.
I wish we knew the prophecy that Rhaegar and Maester Aemon knew. Is is what Melisandre keeps saying or do they have another, Targ specific prophecy? Maybe Sam will find it in the Citadel.