Authur, I've recently been through a similar situation on my 2000 Johnson Ocean Pro 200 hp and found the Rancor fuel filter/water separator was clogged. Before rebuilding carbs, check the entire fuel system from the fuel tank to the engine. Make sure the strainer on the end of the fuel pickup line is clean (you may have junk in the bottom of the tank). Make sure all filters are clean and unobstructed. Make sure all fuel line clamps are tightly fastened. Double check the ends of lines where the clamps hold the hoses to the fittings - the lines will sometimes crack on the ends and let air in. Make sure there are no air leaks around the primer bulb.
A fuel system obstruction (clogged filter or strainer) may cause the primer bulb to go flat when the engine is running at higher speeds. That's a sure sign.
Does the engine have an automatic oiler versus having to mix the oil? If you have a fuel obstruction or air leak it may be oiling excessively (smoking a little extra). When the air motor (fuel and oil pump) cycles thinking it is getting a supply of fuel it also cycles pumping oil - so being starved for fuel it oils excessively. Is the oil consumption out of proportion with the fuel (proportionately more oil used than it should)? That's a possible sign of fuel obstruction. If you can eliminate all of these possibilities, then look at the carbs or the air motor that pumps fuel and oil. Eliminate the simple issues first then move to more complicated = eliminate the inexpensive first before moving to the more expensive.
After going through this same process on mine - it starts easily cold, uses less oil and in the right proprotions and runs much cleaner, smoother and doesn't cut off. No adjustments and no carb rebuilding which is more complicated than it might appear.