The cool thing about having a friend as physical therapist, is that you can call him, explain the situation to him and get a professional answer. :)
So yesterday evening we visited them, and he explained the situation to me: turns out that there is a certain fleece around the muscles in your lower legs, which helps with pumping the blood up towards the heart when the muscles tense up. Muscles grow quite fast when exercising, but the fleece can't keep up, so that it starts to hurt.
He made me pull up the legs of my trousers, and then said: "So, that means that it hurts... HERE!" And yes, the point where he poked me did hurt a lot...
He gave me the advice to take it slow, to stop when it starts to hurt and to keep a day in between sessions, so that the tendons and fleece get some time to recuperate and to catch up. He also gave me (courtesy of Her Majesty, the Queen of the Netherlands!) two inner soles that better support the bridge of the foot -- which is where these sore muscles connect to.
Today I ran 3 x 200m, and then I stopped because the hurting started. I'm pretty annoyed by this setback, but I have some new strategies to cope better. It'll be a bit slower than the program dictates, but once my muscles catch up with my determination, it's once again full speed ahead!