I read on reddit in /Wow that many had gotten the Invitation simply by starting the scenario and end it immediately at Alyssa.
So that's what I did after many months of +700 clears. I got the Invitation 3 weeks after.
It can't be proven, but it is suspected that points doesn't affect the drop chance but If you want the "biggest" chest, you have to gather 425 points. I tried it my self and ended the scenario prematurely at 424 and didn't get max AP token.