It happens that I get a new "welcome" game what is for me the middle of the night. So I see the game hours after the person moved (the non-movers are of no concern here).
My suggestion: The greeters could offer a time period when they are online with a high probability, and get "welcome" games only in that timeframe or when they are actually online.
@Ponderable
This is a good suggestion, and I can't recall (or check right now) exactly how they are allocated - but selecting a greeter definitely should be based on when their moves are clustered. As you have noticed, so many people sign up and then vanish, and this would help tackle that.
@Russ
I do not know what a new member sees when they open an account on RHP.
The majority of my "welcome" games do not even have an opening move from the new member, so I sometimes wonder just what they are expecting to see.
Is the "welcome game" offered as an option to them, or is it just automatically created? Do they even know the game has been created?
Perhaps you need to emphasize that this is a corresponence chess site, so an immediate response should not be expected.
It may be possible to set their "welcome" game up with a greeter that is in their time zone, since we have the option to select our time zone. Matching up with a common language might be helpful as well.
I have been a member of the 'greeter' group for a long time, and for most of that time have been frustrated with how it works. I end up deleting almost every game because the new member does not ever move.