Tip:
Use Hot Corners to put the display to sleep when you put the mouse in one of the corners (I choose the lower right).
When you step away, just move your mouse into that corner and notifications will be redirected elsewhere first. It doesn't even need to be an accurate maneuver, just as long as the cursor is caught in the corner.
Since i haven't used a screensaver in years, I always manually turn off the display like this when I plan to step away for an extended period of time. It's a good habit along side the correct routing of notifications.