Ok, it's simple. To unlock higher clocks, I simply have to set
"/sys/class/drm/card0/device/pp_sclk_od" as well.
To sum up: For my 1209MHz 900mV I have to do the following:

echo "2" > /sys/class/drm/card0/device/pp_sclk_od
echo "s 7 1209 900" > /sys/class/drm/card0/device/pp_od_clk_voltage
echo "c" > /sys/class/drm/card0/device/pp_od_clk_voltage

Works like a charm, thanks for the "Wattman" functionality!

However, I am still not able to raise the maximum allowed power consumption of
the GPU.
It's clear that "/sys/class/drm/card0/device/hwmon/hwmon0/power1_cap" sets the
actual power limit and thus I need to raise it. But the problem is:
- I can't set it higher than power1_cap_max, only values below work.
- power1_cap_max equals to power1_cap, so raising power consumption is actually
completely forbidden
- Despite of being root, I don't have write access to power1_cap_max, unlike to
power1_cap

So, it seems I'm being stuck and there is no way of increasing allowed maximum
power consumption, which is not a problem with Wattman on Windows.

I suppose either I'm missing a boot parameter to unlock write access to
power1_cap_max, or there might be a bug in amdgpu driver.
Any help appreciated.