This is the front diff usually (I hope) although to start withits hard to pinpoint.
Diff whine, and yes, a good description, can be quite awful on a light throttle, and far from uncommon. Thick carpets

One of mine's dreadful, but Jenny refused to admit there was any 'whine hum or drone' for a out a year - now she's finally tuned into it... funny, they supposedly have more sensitive ears than men.
The transaxle diff can also make this racket, removing the prop won't immediately clarify the situation either as diff still turns, but
might reduce it.
First check you can loosen both the filler plug and drain plug of the front diff. then check the oil level, or just drain and refill anyway, observing the drain plug and mayeb sieving the oil (1.5 litres ish), see Syncro website.
Don't necessarily expect damage to the front diff, but just that tolerances and wear have built up as they didn't make that racket when they left the factory - and refilling won't stop it - just worth ensuring it has oil in it.
Dave Aldridge at Shiplake, Henley-on-Thames can reset the pinion clearances, though there is no guarantee it will be quiet until you refit the whole thing, unless its had a total rebuild.
What ratio is it? Syncro berakers may have a quiet one in stock...