Terminology time:
4 stroking - when the engine is "sputtering" or has that "machine gun" feel. Due to having too much fuel (rich)
Bogging - A notable drop in power, without any other strange noises. Sounds like (and feels like) the engine is just spinning down and not producing power. This is due to a lean condition (too little fuel)
Now, the situation you described above with turning off the fuel sounds like it is just normally running too rich. Once the bowl starts to empty, you start to experience a short moment of correct air/fuel mixture and it runs good for a second, then runs out of fuel and bogs entirely.
That could mean a couple things. One possibility is that you are running your oil mix too thin. More oil per part of gas makes the air/fuel mixture more lean. Less oil means a more rich condition. You're experiencing a "too rich" condition, so try a higher oil/fuel ratio? What is yours currently, and how do you mix it?
Another cause can be the needle. It's connected to the carburetor slide with an "e-clip". Move the clip up to go lean, but this only adjusts air/fuel mixture up to about 3/4 throttle.
If changing your gas/oil mix and moving the needle doesn't help, I'll step you through re-jetting the carb.