If the history of both tech and biotech is any indication, GMOs will be massively distributed on timescales much shorter than 10,000 years. Patents last for 17 years, and if drugs like penicillin or acetaminophen are any indication, generic competition springs up almost as soon as the patent is expired.

It's pretty unlikely that the original development of agriculture was decentralized. In fact, we have pretty good evidence that it was intensely centralized in a few places, and that tribes that had this technology then outcompeted, conquered, and killed all the hunter/gatherer bands that resisted using it.