The Wedge K's have this same behavior, especially cold. They got better when the recommended oil viscosity was changed by BMW. Shifting into first often gets looks from other folks wondering what the heck that noise is.
Hopefully after many miles things will smooth out for y'all
I just sold a Wedge K1200 this year. A 2008 GT. You're right the transmissions behave similarly, including gear change klunks 2nd-4th.
Personally, I didn't/don't much care for for either transmission.
One way that they were different is that, with the K1200 GT Wedge, when in neutral at a long traffic light, If I pulled in the clutch and held it in for ~10 seconds, the transmission would silently drop in to first gear (as one would hope it would). Not so with the Wethead, or at least not with the 2 I've owned. You can hold the clutch in 'till the cows come home, and it'll still bash and jolt into gear.
Don't think I'll own the Wethead for many miles (not my cup of tea/already sold my '14 RT)... in fact, I just bought a 2010 Camhead which will probably replace it.
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