Realm First! Illustrious Cook

I'd suggest you grind out Fish Feasts using cheap northrend mats to cut down on how much 450-475 mats you need to get.

Fishing cata fish just got me a 72 hour ban. Wouldnt recommend it.

A "easy" way to try to get this would be to do the newly added cooking daily quests (in SW or Org) with your alts and exchange the tokens for Crate of Tasty Meat (2 tokens for one).
The crate doesn't bind, nor do the meat you could get from it.
Saving tokens on your main to get the needed recipes, you could get the FoS as soon as Cataclysm is active.
Of course you might not get all the meat needed to skill up to 525 and sometimes, you will not get skill ups since some recipes will be green/yellow.

Anyway, I think below is the best one could do to optimize the process, depending on what meat you get from the crates (oh by the way, check the AH too, some people might have realized that too and put the meat there for sale) :

From 450 to 475 :
Cook Salted Eye or Seasoned Crab depending on what meat you have the most
you need to reach 475 for the next "tier" of recipes, but cook any leftover meat as you might get a few more skill ups.

From 475 to 500 :
Cook Hearty Seafood Soup or Tender Baked Turtle
again, you need to reach 500, but you can cook the leftovers to try to get to 505

From 500 to 525 (max) :
Cook Basilisk Liverdog or Beer-Basted Crocolisk or Crocolisk Au Gratin or Grilled Dragon
Depending on what meat you have the most.

Congratulation on your Feat of Strength ! (unless someone beat you to it)

PS : considering that there is about 2 weeks until 7th December, you should be able to get at least 12 token = 4 recipes (@ 3 token per)
and since you need at least 3 recipes (one for each step), you can have only one "spare" in case you don't have enough of one type of meat at any of those steps, basically, the best would be to have only one type of meat everytime, but the RNG won't give you that, so trade meat with friends/guildies if you can or check AH.

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Second path

If you have fishing, an alternative way would be to fish near Cataclysm zones (haven't checked this yet, might be hotfixed), this could prove a better way because you wouldn't be capped on the quantity of fish you can get (as long as you fish long enough).
I suggest to catch at least 40-50 for each step, check Elsanglin for more fishing info.

edit : fishing Cataclysm zones might grant a ban, not worth it, so stick to the meat.