According to Terrence's Chocobo Mechanics, you can go up to 9999 with stamina (divide by 10 to get the value reported by the game), and up to 6000 with sprinting speed (divide by 34 to get value reported by the game). 9999 is a boring value, but 6000 is quite interesting - you don't actually get anything in the FF7 by just looking for 6000/0x1770. Same with 6001/0x1771. When you search for 0x176F however, you get 4 places that say "if bigger than 5999, set to 5999" which sounds good, but I can't actually test it (no save, no time).
If you open ff7.exe in any hex-editor and search for (4 bytes) "6F170000" (which is flipped 0x176F <-> 5999) you'll get only 8 occurances, all tied to the above - change them to something bigger the game would still handle and see what happens when you breed another chocobo. "AE840000" (flipped 0x84AE <-> 33966 <-> 34 * 999) sounds like a good value. If you get higher than 176 on Speed when mating chocobos, you're home. Remember to back-up first!
If anyone with (even basic) hex-edit skills and a little time is reading this, I'm sure he can help you, maybe make this into a patch of his?
