Hmm, you raise some interesting points, but, as much as I hate to do this, I'm going to have to question some small aspects. Anonymous, whoever you are, if you're still out there feel free to reply to these, if you have more answers I'd love to hear them.

Actually 13 chaos emeralds and the South Island ones are the six In this game and were either destroyed at the end of this game or at their last game gear appearance
Yes, that's a credible theory, but that's all. Apart from the fact that the SMC game manual says "discover the emeralds..." Even if they were know about he was still searching for them, and finding them, so it's a kind of discovery anyway...
It's a nice idea, but there's no proof either way so... I'm afraid you've yet to convince me. Also, if Sonic Team had MEANT to show that they were 7 new emeralds and the previous 6 had been destroyed, they would of at least mentioned it. I've never heard anywhere that the 6 were destroyed? Please enlighten me...

Sonic Team probably believes in many gods so this is canon
Just because some Japanese people believe in lots of gods doesn't mean the game does. This is fiction, people often make up settings for their created worlds. Just because Sonic Team may or may not believe in it, it's whether they PUT it INTO the Sonic world that makes it true or not.

First, collect the seven chaos emeralds (as Sonic or Tails) but don't go into the super ring. When you get to Hidden Palace Zone you are holding seven and there are seven on the alters and the M.E., making a total of fifteen emeralds
There are seven grey emeralds looking empty and powerless on stands, and Sonic pulls out his emeralds, they flash and the 7 on the stands flash and look like their powering up, then when you do the stage they stop flashing and glow normally. Yes, they are different emeralds but it is designed to look like it's the Chaos Emeralds power that enters them and powers them up. Plus I'm fairly sure if you don't collect them all before you reach Hidden Palace Zone, only the ones you've powered up are there, but I'm not 100% about that...

...destroyed the Echidnas except Tikal. After Tikal sealed Chaos in the Master Emerald, a god came down from the sky and used the Master Emerald to bing Floating Island into the sky. He then restored Knuckles to the Island (and possibly the tiny animals on the island)...
Um, well yes, Tikal did seal Chaos away... But we have no idea where Knuckles came from, or how the Floating Island went skywards. Yes, maybe, maybe the gods did it, but besides that Japanese manual it's never given us a quantative answer. And saying the gods did it is VERY vague, Chaos was a god, maybe he did it?

Because Super Knuckles can't fly.
Until Doomsday Zone super Sonic couldn't either... Also, very few people accept Super Knuckles and Tails as cannon, they were sort of added extras, cool ones and memorable ones but you might as well ask why Super Knuckles and Tails, and Amy, and Big too since he was there, didn't join in the fight with Perfect Chaos...
A more reasonable explanation suggests only Sonic can go super, until Shadow came along who can also do it as he's "The Ultimate Life Form" and so to intone to the Chaos Emeralds power.

With the Highest Regards
           Swifthom