can't be sure that they didn't discreetly migrated over without the locals' knowledge.... 

...... really doubt so ......
anyways ... seems like you already covered the interesting stuff like the ancient temple complexes and cave exploration
http://discoveryourindonesia.com/15-things-to-do-in-yogyakarta/food wise, I'm not particularly fascinated with gudeg ...... although I find east java food nice (usually around Surabaya for me - like nasi liwet, pecel, rawon) ... but then again yogya is not really east java is it?
maybe can pick up a new skillset for the new economy like making leather sandals or printing your own batiks?