It seems that the simple solution is to place this in /etc/udev/rules.d/99-myrules.conf:
SUBSYSTEM=="sound",KERNELS=="1-1.4.4:1.0",ATTR{id}="CODEC_7300" SUBSYSTEM=="sound",KERNELS=="1-1.3.4:1.0",ATTR{id}="CODEC_9700" Take the KERNELS from udevadm info -ap /sys/class/sound/controlC2, where 2 is the index of the audio card.
Good questions and answers on these other threads:
- Same device name for identical USB sound cards after every reboot
- Udev rules for seemingly indistinguishable devices
This solves it for programs with a dropdown that exposes the ID.