I took a step back and tried what would happen if I try some variations of the original design.
I tried various values for Cff (none, 10p, 56p, 560p, 820p) and found the best results for no Cff (3.34V rms voltage). I also tried the result of higher Ron (75k, 82k and 100k). This did not seem to make much difference, except for the switching frequency. I have the design now working with 82k Ron, no Cff , a 6.8uH inductor and the original 80mOhm ESR 330uF output capacitor. The feedback signal is about 15mV p-p. I tested the design with light load and full load. Under full load, the RMS output voltage is 3.30V, with light load the RMS output voltage is 3.34V. This is quite ok adn within the tolerances of the resistors in the feedback network.
This leaves the question why webench suggests to use a 560pF Cff, as this seems to yield worse results.