Separate tickets means that you are not connecting. Thus, you bear 100% of the risks of a no show at JFK and having to purchase new tickets to HKG at walk-up prices.

There is absolutely no way I would fly and allow 2-1/2 hours (1-1/2 to check-in deadline). But, that is me. All it takes is a bit of weather, a small mechanical issue or a jetway issue, and you are SOL.

If you allow 3 hours for the drive, 1 hour to drop at car rental and get to counter to check in at T-2, you should leave Sturbridge at 04:00. Earlier if inclement weather.

Given the lengthy flight ahead, you might consider flying/driving to JFK the night before and spending the night at one of the JFK-area hotels. Doesn't have to be fancy to be pleasant and really makes the trip more manageable.