You just need to be patient and understand that the game takes time, and if you don't want to wait for your opponents' turn, it's better to decline participation.
As for agreeing on a game, we have several players on our forum who can't even agree on a 1v1 match and drag out all the tournaments until the last moment, and we all know them... And again, if a player has a very limited amount of free time, then perhaps it's not worth exhausting everyone with the wait for a free time slot for the game!
