I think you'll find the data pin expects 0.7VDD, which would be 8.4v, which may be why sending them a 5v signal results in nothing at all. See the datasheet for the pixels here: https://cdn-shop.adafruit.com/datasheets/WS2811.pdf
In a pinch, you should be able to voltage divide an 8.4v supply from your 12v supply. As long as it's roughly between 8.4v and 10v it will fall between the maximum voltage of the logic level converter, and the minimum voltage that the ws2812s consider to be an "on" state.