I suspect it is subtle changes in the amount of backlash in the gear mesh. My Ducati has helical cut bevel gears that were lapped at the factory and have to be shimmed to the same minimum clearance as they were set up to at the factory.
It costs money to lap in and shim precisely gears.
I would have thought it was more expensive to deal with warranty claims, and it still doesn't explain why some do not whine from the get-go, while others do. Unless, of course, the designed-specifically-for-the-M3W-bevel-box is manufactured with such sloppiness that it truly is like a lottery. If so, perhaps Morgan should ask Quaife to up their game and be more precise with their cnc routing.
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Gears whine because the gear faces are hitting each other taking up the clearance differently as the gear rotates. Round is not always perfectly round.
It should be, as it's CNC'd. It can certainly be done, and I very much doubt a big company like Quaife doesn't have the machinery.
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If the clearance is less, and you are lucky with nicely matched gears, then the box will be quieter, but still whine. Too much clearance and you get clatter on neutral throttle which is the noise of the gear faces slapping against each other on each side.
In other words, it's down to pure luck, and lapping the gears won't do, as you first suggested. Seriously, we live in an age of CAD design and CNC machines which can take the cad files directly. It can be much more precise than some guy in a shed, and it is now down to "luck"? It may be, but it shouldn't be. Bevel boxes are everywhere, and it's not exactly cutting edge technology having a bevel box. Hell, Ducati and Harley Davidson have bevel boxes. Yet you don't hear them having whining bevel boxes to the extent that the M3W seems to have.
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Straight cut gears hit across the whole straight width of the gear providing a wide contact line that does its best to roll around the involute form of the gear surface, whilst helical cut gears slide against each other along the length of the gear; so its a softer transition of forces. Hence less noise, but weaker gears.
Yes, and all this should be no problem for a company like Quaife to take into account in the design and CNC cutting phase.
What I'm saying is that it doesn't matter how many potential problems you can list. The fact of the matter is that 1) bevel boxes work without whining in other vehicles, 2) Changing bevel boxes under warranty for what may be another faulty one (if it truly was a matter of luck) cannot be cheaper than doing it properly the first time around, and 3) A company like Quaife ought to have the knowledge and machinery to fabricate a bevel box without the whine. But as it's down to luck, perhaps they can't and it's impossible to do.
So, the cheapest and easiest solution for everyone would be if Morgan swapped the whining bevel boxes before they left the factory. It would be less waste of resources all around.
