I'd like to pint out that if you given us a proper schematic drawing instead of a BS kiddie drawing a great deal of ambiguity and back and forth nonsense could have been avoided.
So, how about a 74HC173? It's a D-type latch, parallel-in parallel-out, and it has an output enable to which you could connect the PWM (tristate, so you'd need pulldowns). Or a 74HC573 or 74HC574 which would give 8 channels. In each case, inputs are all together on one side, and output all together on the other side.
But if your data was serial, you could accomplish the whole damn lot, 8 outputs at a time, with a TPIC6B595 https://www.ti.com/lit/ds/symlink/tpic6b595.pdf?ts=1617311501983&ref_url=https%3A%2F%2Fwww.google.ro%2F