How to frame incomplete previous studies when applying to new graduate school without being too negative about previous program?
what is a convincing non-negative way of explaining "I don't have references from my prior program?"


If you dwell on it, it will sound like you're making excuses. It's not really worth spending more than a sentence describing unfavorable circumstances that made you leave this place or that place. It might even be better to not mention at all. Just make sure you have favorable references from somewhere to go with your application.


  is there any way to get connections made between "gifted" and "promising student"?


Through achievements. If you say "I am good at X," no one cares, or really believes you. If you say "I did A, B, and C," it's good if you can say "I received award Y," by pointing to things that demonstrate that you are good at X, then you will look good. Talents only count to other people if you use them to achieve results.