1986 isn't long. In reality, it shouldn't matter if you make the chain 10 million diodes long, unless you need to refresh it continuously because you are showing scrolling text or an animation.

The important thing is to have a design that scales. The PSU has to be powerful enough that it can handle the load. Having ten times as many diodes just means that the PSU must be able to handle 10 times larger currents.

And having multiple cables from PSU to diode boards will make sure that the cable capacity will scale.

Having enough capacitors on the driver boards to make sure that the driver chips gets acceptable supply voltages will make sure that the design can scale without need to bother with the total number of boards. Each board just has to be able to hold its own.

You must have acceptable signal quality for the signals to the first board. But it is then up to that board to make sure that the signals are ok to the next board. Being digital, the problems with the clock, data and latch signals should not scale with the length of the chain. The only thing required is that every single step holds its own, and supplies acceptable levels and flanks to the next receiver in the chain.

The only advantage of driving the display with 8 shorter chains instead of one long chain is that the processor can emit a byte at a time, instead of shifting out individual bits. But it doesn't matter to the signal quality.

In the end, the design should make sure that the data reaches through the system with zero transfer errors. The ability to scale infinitely and still having good enough signal quality that you can have zero transfer errors is one of the advantages of a digital world. Just as long as every single step of the chain fulfills levels, setup/hold times, rise/fall times, and each chip is properly powered so its inputs will really be able to operate according to the datasheet.

Having an octopus from the power supply, and having ample of low-ESR capacitors on each board to handle the current ripple is the main thing to focus on.

Have you computed the amount of energy the diodes draws in relation to the switch frequency of the PWM? Are your capacitors big enough and with low enough ESR to feed the diodes for a significant part of a PWM pulse?