How do I get into the central corpus of Buddhist teachings given the short time I have until I leave.

If the time span is only six months, then I would recommend really hammering home your understanding of śūnyatā. To this end, if you have not yet looked into the MMK and ordinary Ngöndro, now is the time to get those basics down. Honestly the likelihood of one month there resulting in some kind of 'test' of this approaches zero, but assuming you already have some establishment in Buddhism, in six months, keep it simple: dependent and interdependent origination, svabhava and its lack, the basic premise of Buddhism (the four noble truths), etc. This sounds like I'm suggesting the ABCs, and I am, not because "you're not ready," but because in Buddhism the ABCs will get you very far. Many of the supposedly most profound teachings are means by which to fully understand, fully grok (not just think but feel, ideally not just emotionally but even physically!) the very basics. The "rest," Dzogchen included, is not so far off if your time is spent coming to understand interdependent origination.