So, I’ve done some tweaks to the prototype… namely fixing some wire assignments. I also had to drop my 1kΩ resistor on the input to a 100Ω as the voltage drop of the 1k was too high.
At the moment, I am seeing ~3V at the MCU, which is good enough.
Beneath the afro of wires, is the prototype.
… and this is the PWM LED control in action (animated GIF). So PWMing the output enable of a 74LS374 works, and doing the same on a 74HC574 should too.