I don’t think using the 4 channel level shifters are going to change anything. I would try different resistor values. I would highly suggest trying 33Ohm. Most prebuilt controllers use 33 Ohm resistors, including the ones that cost hundreds of dollars (Kulp, Falcon, Etc…)
I have a 2,400 Pixel Mega tree running off of 6 outputs on an Esp32 using a SN74HCT245N level shifter (and 33 Ohm resistors) Plus a 7th port running a 90 pixel star and a 70 pixel spinner. There is never any flicker.