[werk_ag]

CS10, though, is showing much slower rise/fall, ...

This is normal as the CS10 signal doesn't pass through the logic level converter, attenuation is done only by a resistor.

There is something strange with the voltage levels. As the Arduino Nano is powered by only the USB 5V, and there is always a small voltage drop (0.7V) at the schottky diode, how could you get a Vpp of around 6.24V?

Despite the voltage readings (you should check that) the pics show that the logic level converter is doing its work.

I'm inclined to say that the problem is with the cables or even with the display.

What voltage do you get at the 3.3V pin? This is the reference voltage for the output of the logic level converter, and it will not be higher than that value.