Thanks Glen for the additional details. That slightly older 3.8.34 version linked in this thread seems to work fine. It looks like the official driver is 03.08.54P as you said.
I did find another way tonight to solve this problem.
After using the 16900-14121 recovery DVD, with a $20 Amazon SI3114 card (which we've determined is not directly supported in the recovery image), Windows XP blue screens with the 0x7B stop error. This is why I was investigating doing essentially a ground-up install. This works fine.....although it requires a couple hoops, and gives something less than the official version. I did this previously with my 16900A, and practically speaking there's no issues.
Tonight, I decided to try to fix the broken Windows XP recovery install and have what I believe is a great solution.
https://superuser.com/questions/1738250/recovering-a-windows-xp-system-gives-error-0x0000007b-in-the-bsodThis solution uses Hiren's Boot CD version 15.2, which is available here
https://www.hirensbootcd.org/old-versions/After using the recovery disk, boot this "boot cd", using the very cool mini XP environment, use the "fix hard disk controller" option. It boots in a minute or two, and the fix is essentially immediate.
Then, just eject the disk, and reboot.
That's it. The LA will boot normally, go through the Windows XP setup wizard, and off you go.
Hiren's had the 3114 drivers "built in", which was convenient for my purposes, but I noticed an available F6 option for adding drivers via floppy, which would help if you were dealing with an HDD controller that isn't directly supported.