thank you for the answer. I am a bit surprised that caps on the LCD_DATAx are helpful. My understanding is that they must slow down the edges because the AM335x drivers are forced to charge them, what just takes time at a given AM335x buffer strength, 6 mA in this case (data sheet Table 2-7, p.26).
I was thinking that much the same effect can be had by adding series resistors in front of the LCD inputs of the TDA19988. The slowing down would be due to charging the TDA19988 pin capacitance through the resistor. I am curious why it did not work in your design. Perhaps I will give it a shot....