In fact it seems that controlling the fans on my card using the ADL Overdrive6
api doesn't work. 

But it works using Overdrive5. When I modify Olegs test-program to use
ADL_Overdrive5_FanSpeed[Get|Set|ToDefault_Set]() api indeed my fans react.

So the next thing I guess would be to check the mmio-traces. In fact for me
personally already the equivalent of ADL_Overdrive5_FanSpeedToDefault_Set()
would be sufficient, since it seems to put the fan automagically to a good
minimum.