Kalliste: After seeing a shot you would like to save be very quick and click on MENU (below your name in game window) then scroll down to REPLAY SHOT then on bottom of the `shot window` >>> there is SAVE...SHARE...EXIT.....so click on SAVE or you can click on SHARE and send the shot replay to your OWN email address. Then when you are done just click EXIT.
Good advice for every shot!
Even quicker and an advisable step in MP games is the "Copy" option close to the link display itself - one click and saved for further treatment in a text editor and/or WGT blog.
I also think that the other players have no influence in the timing - the game itself cares to bring you through the scorecard display and to the next tee.