I've had three versions of that engine and never suffered that particular regular "cough"... the most common one is an initial cough as you open the throttle from idle.
You may have hit upon the answer by chance but...
Important to know spark plugs are good and correct grade... also that fuel is weeks/months and not years old... and the correct mixture of proper 2-stroke oil... not something drained out of the lawn mower (I know you like to experiment).
Ideally timing settings should be checked as per the manual Max linked but they are rarely wrong so you could skip that.
Setting the idle and mixture speed should be done in a tub or on the water not on muffs.
OB should be warmed up and make sure choke/fast idle is backed right off. Best if you have a small tach to know the speed you are setting.
OB needs to be in forward gear and start with the idle mixture screw wound in clockwise to gently seat and then out 1.5 turns for a basic position. Set idle speed to 750-800 rpm.
Turn idle mixture screw in gradually until the revs drop and it hesitate and note this position of the screw. Then turn out screw until it hunts and revs drop noting position. Set mixture screw to a midpoint of these positions. Stop engine and screw mixture screw in until it gently seats and note how many turns in this is then turn back out to the midpoint.
If this midpoint is about 1.5 turns out then often any coughs or sneezes can be eliminated by turning out another quarter of a turn (anticlockwise)... if the midpoint is around 1.75 turns out that may be fine but you can always try another quarter turn out if not.
After this recheck the idle speed (in forward gear remember) as it may have risen.
If the coughs/sneezes continued I'd be having the carb apart for cleaning and new gaskets.
However this is what happened to my Mercury 15hp and I've not seen it mentioned on the net elsewhere... post #8 here...
If that pipe was just starting to split and opening/closing with engine vibration it could cause an intermittent weak mixture.