My understanding is that the GY6 is only found in Chinese scooters, and only 150cc. The Buddy is built by PGO in Taiwan, and is likely to be completely different. If the damage was cause by running it without final drive oil, it may not be so complicated after all. Probably does not involve the engine or even the variator. Most everyone on the Zuma forum recommend UNDERFILLING the final drive on Zumas and Vinos. I slightly overfill mine. It is vented so it won't blow a seal. And I have never had any oil blown out the vent.
2002 Vulcan 750, 2001 XT225
2008 Vino 125, 2009 Genuine Stella
2012 Zuma 125, 1980 Puch Newport moped