Hi Matt, and welcome to Justanswer. My name is XXXXX XXXXX I will be helping you today. If you need clarification on something please post back here.
It does sound like you have a case of clogged carbs. But before you jump into tearing the carbs apart, you should still go through the motions.
If you brought this engine to me here is what I would do and the order I would do things in.
1. Compression. Your results should be about 100psi or better, all cylinders should be within 10-15% of eachother. You did not say what you got for a reading, but that is what it should be.
2. Spark. These are the testers we use in the industry.
But you can also get cheap spark checkers at most good autoparts stores.
You need to hook the spark tool up and set the gap to 7/16ths of an inch. The spark should easily jump that gap, be hot and blue in color, and be consistant with engine rpms.
If the engine runs good when cold, but cuts out when hot. What I would do is run the motor until it starts to fail, then check spark again. I will either have good consistant spark or I wont.
I would also check and set if necessary the base and advance ignition timing.
I would check the quality of the fuel itself. Either pull a sample of it and put it in a clear jar overnight. In the morning, look for any kind of dirt/debris/water in the fuel, or any kind of seperation line.
Or, Get a small outboard tank (like a 3 gallon) and fill it up with known new fresh gas and try it.
Lastly, if compression and spark and fuel quality check out, then the problem is going to be in the carbs. Carb jobs are very common on marine engines. They make up 80+% of all my work. It takes a piece of dirt the size of a piece of sand in there to gum up the works. If the carbs were cleaned in the past and cleaned well, but hooked back up to a dirty fuel system, they will clog again pretty much right away. When you do these fuel system jobs you go through the whole fuel system, from tank, to pump, to carb. If I do a fuel system job for somebody, and they do not have one, I install a fuel water seperating filter kit to try to keep these problems from happening again. The filters in the engine are equivelent to filtering fuel through panty hose, the external filter kits filter down to about 10 microns, and they will seperate water, they work much better.
That is my method to my madness, it has served me very well. Its nothing new, an old timer taught me to troubleshoot in that order, and thats the order that has always worked for me.
Also, the troubleshooting method above will help you find 99.9% of the most common problems in an hour or 2. There is always a chance you have an oddball problem, but that would fall into the last .1%.
Post back here with any additional questions or concerns my friend.
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