The settings work. I still need to set register 0xD6[7:6] to 11 (HPD is always high), but I no longer get a black and white image if I do this and the transmitter will start by itself.
It is weird that I have to set HPD to always high, as the pin is high. One thing I did not do though is connect any of the CEC signals and as already said I forgot to wire the +5V DDC. Perhaps there is still an issue because of that.
I am in the progress of making a new board. On this one I will wire the +5V DDC. CEC can be left out again.