I believe you’ve found a good part of the origin of the problem. What I want to bring up is where do you think the missing parts went? My guru mechanic in TN told me of this in a motor. He worked on. A lot of the time they can be lodged in different placer within the powerhead causing hot spots from low or no water passage. That’s the worst one I’ve seen from someone I know. My Mariner went 8+ years before I changed it and it wasn’t pretty and started losing chunks. Check seals while you’re in the neighborhood. Shifter shaft and power shaft.
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