Well, I got SOMETHING to work... however, it took some time to figure out how to get one Pokemon's nickname changed. I ditched the Blaziken because it was giving me bad luck, and grabbed another one of his Pokemon I had nicknamed (a Groudon). First (just as a test) I managed to successfully change the IVs and PID of the Pokemon without touching the nickname and OT, and it came out legal. I could also change the letters of the nickname, but not the amount of letters. Anytime I changed the amount of letters in the nickname or unchecked the flag for the nickname, the OT trash bytes got messed up.
What I ended up doing was finding another one of his Pokemon (Same OT) that had NOT been nicknamed, and had the same amount of letters in it's non-nicknamed name as Groudon (in my case, I found a CASCOON). The "trash bytes" or whatever the things are with the slashes after the OT name were different in the CASCOON vs the nicknamed Groudon... so I just copied them (they were \FFFF\0138\FFFF on the CASCOON instead of \FFFF\0156\FFFF on the Groudon) and replaced Groudon's OT thing with that. This allowed me to uncheck the nickname flag and successfully change Groudon's name back to GROUDON (also had to add \FFFF\754D\0207\FFFF after GROUDON, I was just copying what CASCOON's name had too) and everything checks out with Pokecheck, including the OT Pal Park trash bytes.
So yeah... I tried the same thing with Blaziken, I found a CORPHISH that was owned by him and did not have a nickname... replaced the \ \ bits in the OT of Blaziken with Corphish's (happened to be \FFFF\013D\FFFF) but unfortunately... I didn't get the same result as I got with Groudon, Pokecheck still says the OT has invalid trash bytes. SIGH...
Next thing I did was try to see if I could find another kind of correlation besides just the length of the Pokemon's names... My idea was that Groudon and Cascoon worked cause they were both wild pokemon, Blaziken was a starter... So I took EVERY Pokemon I had that came from either Ruby or Saphire... I took each one's OT with the crap after it, and recorded their name or nickname if they had one, put them all in a list and tried to find a pattern. There was sort of a pattern, although it wasn't perfect... I tried using the pattern to change my nicknamed Kyogre back to regular KYOGRE and it worked! Just like Groudon (And yes, changing the nickname without changing the stuff in the OT made it not legal).
So, I had to do one more test... I had a Swampert, it was my starter from Saphire and it was also nicknamed. Swampert has 8 letters just like Blaziken, so I tried the pattern that I had for Pokemon with 8 letters (the stuff after the OT happened to be \FFFF\013X\FFFF, where x was either 6-9 or A-F) and I landed on X = C and it worked. Great, so I tried the same thing with Blaziken.. went through those combinations, none worked. Sigh... Unfortunately I used all my 5 letter OT names with Pokemon caught in Ruby/Saphire, and that's the only pattern I saw with Pokemon with 8 letter names... I suppose I could also look at all the Gen 1 and 2 Pokemon that came from Fire Red/Leaf Green because those came from the Pal Park too, but I'm starting to get lazy now =P
The only way I found how to get around it was by changing his OT name to a longer name (If it's 6 letters long, it always ends in \FFFF\FFFF. I didn't try 7, but I would imagine that would eliminate that ending crap altogether and it would just be the 7 letters). I don't want to change his OT name though =P And yeah I tried putting just a space after his name... Pokecheck doesn't like that: "OT name has leading/trailing spaces" Although it's only in orange text, so I guess it's still legal?
So I guess there's just something out there that doesn't want me to change this Pokemon's nickname =\ I wish I knew more about what was going on with this numbers and letters so I could figure it out the right way instead of all this detective work. I did learn that there seems to be a lot of Pokemon with names that are 7 letters long though.