This works fine, except for leap years (the day of the week isn't shown.) 2016 is a leap year, but 2302 is not. Presumably David Braben is planning to continue to support the game for at least two years, so why not start with 2314? Then the problem doesn't occur until 2100/2400.
What about leap seconds? Well, the median solar day is currently increasing by about 1.7ms per century. The net error in 300 years should be around 280 seconds, big enough to notice! But you can just pretend that the ITU (or successor organization) made up its mind to abolish leap seconds, while strangely keeping the Earth calendar.
I suppose future-ITU could also be deemed to have change the leap years for the sake of game consistency as well. :)