Congratulations on expanding your influence in the happy AMEX family!
Don't sweat the Green Card denial, you simply ran afoul of the AMEX 90 Day Rule: No more than 2 credit card approvals in a 90 day period. You got 2 credit cards and should have been approved for the charge card as well, but sometimes they will not approve more than 2 applications in a single visit - regardless of the fact that the 3rd card was a charge card and not a credit card.
Wait a couple months, after these cards post to your CR. Then app for a charge card. I wouldn't go for the Green Card becuase of a lack of real benefits. I would suggest you app for the Gold PRG Charge card as the underwriting is the same as for the Green Card and nets you MR points and other benefits.
Remember to remove your shoes as you enter the AMEX clubhouse - we are a civilized bunch around here!
When on my Amex account, clicked on a few cards and when I attempted to apply 2 cards stated I was pre approved for Delta Platinum and Starwoods SPG. Applied and was approved Delta $1400 SL / SPG $1000. But denied for Amex Green charge card