The first cycle of cooling the tank has begun today.
After having some trouble with the calibration of the temperature controller and a sudden (and still unexplained) problem with the pressure meter, we are now cooling the tank.

The rate of cooling is now approximately 0.07 K/min at an inside pressure of 2.2*10^(-4) Pa.
With this rate, the cooling down to 10 K will last at least 2,5 days (even more is expected when the temperature falls below 70 K and freeze-out of the remaining gas appears).

I think of using He gas in the future that could be injected into the tank for increasing the effectivity of the cooling process.

Attached is a photograph of the temperature and the pressure controller at the beginning of the cooling cycle, right after the cool-down has started.