Well...no more stressing about it....the local Customs & Border Patrol office called me back to tell they are booked through June.....so I will not have enough time to get the GE before this trip.
So I will trust United (eek!) and hope for the best.
Thank you for all you helpful information!!
Why won't you have enough time? I got global entry last year, I applied on line and got the interview I was approved at the time of the interview so if you can get a June appointment you are fine for a mid July trip.