I'm not sure what Global Entry has to do with your domestic-international connection.

But I'd like to comment on the nearly 3rd world conditions we experienced at JFK immigration last week, while making an Int'l-Domestic connection. Arriving in the T-8 immigration hall, the regular line looked like it would take an hour or more.

And the GE line was 25 deep, because out of 8 GE terminals available, only 2 were operable. On the rest, the screens indicated "Out of Service". It took us about 30 minutes to make it to one of the terminals, and by that time the GE line was 60 to 75 people deep. I shudder at their wait.

BTW, those with tight connections and the coveted neon orange card were given no consideration by immigration. Even with GE, they were forced to the back of the line.

Exiting customs into that sad, crowded, narrow passageway out to the street, we looked all over for some decent signage for getting to domestic departures. We were rushed, and instead of searching for an escalator, we ended up at the one working elevator up to departures. Another line of people with carts full of luggage meant waiting through 3 cycles of elevator up-and-downs before we were able to squeeze onto one.

I do a couple of international connections through JFK every year (which I've always found preferable to MIA), and I don't ever remember it being this bad.