Success! (at least mostly). Thanks to The Headacher. Wouldn't have found that documentation without the pointer.
Had some trouble figuring out which chipset I had - looked up lspci -nv, vendor/device ID, then realized it was sitting in front of me every time I started alsamixer up the top. Mine is ALC262. Most of the entries under this chipset in the documentation were for other makes and auto was the default, so I tried basic and suddenly all the mixer apps had all the controls activated, and sound worked from the speakers as soon as I started X. The only problem is that the headphones control which comes from the speakers and moves to the line out when plugged in is too soft even at maximum volume, but it is easy to turn up another control (Front). That doesn't get muted when the line out is plugged in but this is still a huge improvement
To test different model options I had to get out of X (ctrl-alt backspace, still works even though I have runlevel set to 4, just don't log back in)
change to text-only screen (ctrl-alt-F1)
# rmmod -f snd_hda_intel
# modprobe snd_hda_intel model=basic
Now I can load this at boot.
Thanks again. This has really been bugging me.