I've somewhat improved the display flicker by changing the SC189Z power supply configuration from a 2.2µH inductor and 10 µF output filter cap to a 1µH inductor and a 22µF output cap. That has helped, and has been what's been going out to purchasers for most so far.

But I decided to see if I could do better, and I found another buck controller on DigiKey that is pin compatible and has specs that are good enough. It's the PAM2305AAB330. It calls for a 4.7µH inductor and a 10µF output cap. I swapped one in and it appears to have made a big difference. At full brightness, there's no discernible flicker at all. At minimum brightness, there still is some, but it's not bad.

It also doesn't hurt that the PAM2305 is half the price of the SC189.

So, that's what's going to be used from now on. I'll save the SC189s for the GPSDO.