Final Fantasy Legends: Hikari to Yami no Senshi is a completely original game. New world, new characters, new music, all done in the style of 16-bit era Final Fantasy games. It seems to me that this is exactly what you're looking for; the only problem is that nobody outside of Japan can play this game yet. If After Years is any indication, this game will most likely get some kind of port to a more accessible platform.
And I did play the After Years and I thought it was just fine. I like the new characters and story, and adding the phases of the moon affecting battle conditions was a nice touch too.
You haven't played After Years or Legends, yet you call them "half-baked" and make assumptions about the amount of "effort" put into them. What makes you think that an internet petition is going to get Square Enix to sit down and say, "Guys, we need to put more EFFORT into making a 16-bit Final Fantasy game! We need make sure this game is fully baked!" What makes you think that just because you get 100,000 people to sign your petition, Square Enix is going to make a better game?
I didn't want to say this before because it's something everyone says about internet petitions and also what you were petitioning for already existed, but here's the thing: internet petitions don't work, especially not with such a traditionally Japanese company like Square Enix. 20,000 people signed a petition for a Final Fantasy 7 remake and what did they say? "We have no intention at this time." That's an official response made to any inquiry made about unplanned or unannounced projects, and doesn't really have anything to do with a petition or the amount of signatures on one.