Can't help you at all with the gear, but some random thoughts..
We'll take whatever we can get at this point
The strange noise during a hard turn could well be cavitation...
That's what the Admiral thinks. To her, and her hearing is much
better than mine, it sounded like a continuous version of what we'd sometimes hear when motoring at cruising speed when out on the lake and running across a large-ish wake from a power boat. As we'd cross the waves, we'd hear a bit of what sounded a bit like cavitation noise. The prop on our boat isn't all that far below the waterline. It was trivially easy for me to get to it when I dove on it last Saturday. I just took a breath, sank down a little, and pulled myself down to the prop via the top of the rudder.
the rest of it makes me wonder if somehow the prop is not fully opening and may occasionally try to refold even under power...
Nobody I've talked to, so far, seems to know much about folding or feathering props. Certainly I do not. But a folding prop, like the Martec we have, seems like a pretty simple mechanism. Centrifugal force thows the blades out, no? In forward: The action of the blades against the water tends to force them forward? This is (one reason) why reverse is so much worse with a folding prop: Because all that holds the blades out is centrifugal force, and the direction of trust is actually trying to fold them?
Do (Martec) folding props have a failure mode such that, in forward, they tend to fold up, or one blade wants to fold up, under forward thrust? That would explain everything, I guess.
this is unusual but could account for the increase in rpm without "popping out of gear", as well as the sense of loss of power while motoring.
Thing is: When the engine goes unloaded, I don't recall hearing cavitation noises. Then again: The engine is revving and your mind is reacting with "Holy sh*t" and has you heading for the throttle with all due speed.
Btw: When an A4 clutch assembly slips, nothing actually pops out of gear, it just slips until and unless you reduce power so the coefficient of friction takes over again.
Could there be something in the area of where the blades are pinned that you missed on inspection?
It's possible. The water was exceedingly murky. The prop, blades, shaft, etc. were all just a murky shadow. I felt all over with my hands, as best I could. But there was no way I could actually see anything clearly.
Alignment issues would cause vibration and unusual sounds as well, but if it's bad enough to slow the boat down the vibration should be quite excessive and leave you no doubt about what the problem is.
Furthermore: You'd hear, sense and feel it at all
speeds and under any thrust conditions, wouldn't you? If we power slowly and gently, reaching no more than, say, 4 kts, she feels pretty decent. Well, she used to. I'm pretty sure the problem is getting worse. On the way back this last time, anything over 3 kts felt wrong.
Also I wouldn't expect alignment issues to occasionally "unload" the engine.
Nor would I, but I've little idea of what I'm doing, anyway