If you ever tried hitting the choke while it was dieing that would tell us for sure.
Hi speed jets are not hard. Top two carbs are easy once the airsilencer is removed (lots of screws). You should have direct access to the carbs. You can check the top carbs without removing them. Take the plug out of the bottom of the bowls. 7/16 wrench. You should have fuel drain out. Be sure and disconnect fuel line so it does not continue. Once the plug is out you will need a very small straight screwdriver to go into the hole that is left. They make a special tool for this, but I have done it with a small screwdriver (might need to grind it down to fit). Unscrew the jet that is in the hole and inspect. You can run a small wire thru it. I am usually able to blow them out with a compressor. Be sure and do all three. You will probably have to remove the bottom carb to get at the drain. If you find one or more plugged that was the problem. Reassemble and be sure to use locktite on the small fine threaded bolts on the air silencer, you do not want them to fall out and be sucked into the engine. I would then add some quality fuel additive to prevent it from happening again. Alot of the time this is all you need to do. If they are plugged real bad and either no fuel comes out of the carb when the drain is pulled or you get dirt out. I would suggest pulling the carbs and having them cleaned and rebuilt.
Yes that is the hole the one right below the airintake take the plug out and the jet is about 1.5" inside that hole. The jet will unscrew right out the same threads that the plug uses.
The choke is the outermost moveable plate in the throat of the carbs. All three of them are linked together on the starboard side and controlled by the solenoid.