The exhaust system 'shouldn't' have anything to do with the engine itself overheating. The purpose of injecting raw water into the exhaust elbow is to keep the exhaust header cool and carry the exhaust fumes through the loop and downward (where non marine systems rely on a more or less straight path). Marine systems are somewhat contradictory to typical performance norms in diesel systems where maintain exhaust gas temps helps them flow faster... that said there still has to be some amount of system back pressure to function properly.
A secondary, but I would guess almost equally important, feature of a wet exhaust keeping the exhaust manifold cool is to keep overall temps in the engine space low. You'll notice that dry exhaust systems have insulation wrapping, and some wet systems are wrapped from the exhaust exit flange up to the point where the raw water is injected.
As pointed out by others above, if the engine itself is overheating is more likely to do with a damaged or underperforming raw-water pump as well as any component that is in line with that, including the raw water strainer. Its good you identified the build up in the exhaust elbow and cleaned it, but that same kind of salt/mineral deposit/general junk can build up in the heat exchanger (if you have one).