This past Sunday, there was a new little box in the upper right corner of the first invite I received while already in an ALT game. It said “Visible to friends.”
I do not know whether you are a mobile player now but when I first knew who you were, last Christmas, flash was still operating, and I assumed you were a PC player.
Anyway, that box that allows visibility has been there for a while (way before last update), at least on PC. I do not always see it but it may be because I simply didn't catch it. I do know that when getting an invite and declining, it would pop up across top of screen with the option of checking the box.
Currently, when friends see me "green" and want to invite me to game, they will send a PM asking if I am available. Prior to last update, I was constantly opening the window with my profile and checking to see if I had messages. Now, since the last update, PMs are forwarded to my Gmail account, so life is easier.
Now, when in game, I will get an alert from my phone that I have mail and can see that someone wants to play, and I can then respond.
So, it appears, slowly fixes are being made and that is a good thing.