I've noticed that the firmware extensions (e.g., firmware-atheros.tcz, firmware-mediatek.tcz, etc.) do not have a startup script. However, device drivers (e.g., ath9k) are able to find firmware files early in the boot process without any problems.
In TCL, things that need to be available very early in the boot process are usually made available by an additional, custom initramfs. It seems I'm missing the magic sauce in the TCL boot process that ensures firmware extensions are loaded before device drivers need the firmware files.