Concerning the Final Summoning as the only way to defeat Sin matter, I don't think that sounds like an inconsistency at all. Yes, they penetrated Sin's armor and reached its core with just their weapons and magic once before -- but that was also while it was subdued and kept relatively docile by Jecht, whose humanity was pushed to the forefront of his mind by the Hymn of the Fayth. And the song only worked because he was particularly fond of it.
It was a unique set of presumably unrepeatable circumstances.
It also does stand to reason that a Final Aeon could legitimately destroy Sin now unless Yu Yevon has been called back as well. If it's just the monster, a Final Aeon could do it.
It didn't work in the past not because the Final Aeons lacked the power to defeat Sin, but because Yu Yevon would possess them and use them as the core of a new Sin once the job was done, burning out the aeon's fayth and killing the summoner in the process.
Of course, if Yu Yevon was called back as well, the Final Summoning would be useless.
As for why it's more powerful than a regular aeon, Yunalesca explained that in the original game. It has nothing to do with the sex-fayth method and everything to do with the bond between the summoner and the summoned. She says that bond could exist between any two people. It's the bond between friends, parent and child, lovers, etc. That's what gives the Final Aeon its power and makes it more powerful than that same aeon would be if summoned by a different summoner.