Removing the diffuser layer significantly improved the keyboard backlight visible brightness. That’s all.
It’s still uneven as hell, but at least I can see all the keys.
I also tried coating the keyboard PCB with reflective paint and covering the tops of the backlight LEDs. It improved light distribution just a little (not shown in the photo). But removing the diffuser film gave me the best result-to-effort ratio.
The “diffuser” film:
It should be a thick light-guide film, not a 0.1 mm diffuser. The LEDs should be oriented to emit light into the light conductor, and the PCB should be reflective rather than black matte.