I am a current HAI student (very near the CFI checkride)
HAI is a great place to do the J1 thing. While the numbers dictate that not every graduate of HAI will end up working at HAI, so far I have seen every J1 student get a job somewhere in the US (if that was their goal).
Since HAI is also a JAA training facility, if someone on a J1 visa gets work there, they can then train toward their JAA license while they work as a CFI.
So while you can't count on getting hired by any school that trains you, if you put in a good effort and stand out as a student, pilot, and CFI candidate, there's no better place for opportunity than HAI.
(Can you tell I like the place?)