Unfortunately we don't have the arch linux feature in tinycore (yet) so you can't use the hack from the website ;-)
The modprobe from coreutils (tinycore extension) supports something like
option snd-usb-audio index=0
option snd-hda-intel index=1
in the /etc/modprobe.conf file, but I don't know whether the builtin busybox version supports that.
If that fails you can use
blacklist snd-usb-audio
blacklist snd-hda-intel
and load the modules yourself with "modprobe snd-usb-audio" in /opt/bootlocal.sh. Then the ediroal device should always be hw:0 and after that you can do modprobe snd-hda-intel, the nvidia should be hw:1