Hmmm, I'm scraping the barrel for ideas now, but I have got one. Your use of the word 'whirring' is interesting. I;d been thinking it was more of a clacking sound, which is what mine was making. But whirring is a bit different.
A friend has a 3TA. He had hassles with oil spewing out everywhere, including the gearbox. He fitted a gasket behind the inner cover, which helped reduce the leakage, but since then, it has made whirring noise. He demonstrated it when he rode it over to mine the other day. My thought was that by fitting the gasket, the mainshaft has been moved several thou to the right, making the primary chain sufficiently mis-aligned to cause the whirring sound. The only problem with applying this theory to your bike is that his whirring occurs with the gearbox in neural whereas yours only occurs when in gear and the clutch engaged (therefore, when underway).
I suppose there's more tension on the upper run of the primary chain when in gear and pulling, which might make the noise a little bit louder, ie: enough to be heard? Could it be something like this, do you think?