Bidirectional level shifters, especially the ones with 1 mosfet transistor and 2 resistors, are horrible for WS2812. They have different speed for rising vs falling edge which distorts the signal which is terrible for WS2812 where the width of pulses matters. Many of them also have very slow rising edge speed, far too slow for a fast protocol like WS2812.
We make this board for the level shifting. It has the best type of level shifter, and impedance matching resistors that really help with signal quality, and it works with CAT5 or CAT6 cables which are the best type of commonly available wire to use for the signals.
I highly recommend you use this. It greatly improves the odds of a successful project. For use with Teensy 3.6, don't forget to also buy the sockets and taller pins, since Teensy 3.6 is longer and needs to be mounted higher.
Your diagram also doesn't make any sense. You're showing the ground as green wires, but there's a black wire for negative. The negative output needs to be used as GND for Teensy and for the level shifter. The level shifter will also need the positive power connection, so it can output a signal at the correct voltage. Even with a good unidirectional level shifter, it can't work as you've drawn those connections.