What you would have to do is clear the DMI memory pool. To do that you have to use QFlash again and then on the main screen disable Keep DMI Data
Instead of re-flashing, I just cleared CMOS (via the button), and then I was able to get AHCI to work. Plus that totally fixed the S3-delay problem. It now resumes from S3 in 3 seconds instead of 40! (I had tried the clear-CMOS button earlier, and it didn't resolve the S3-delay problem, so apparently it was AHCI mode--not just clearing the CMOS--that fixed the S3-delay.)
Of course, there really shouldn't have been such a long S3-resume delay even in the default IDE mode. So that's something that Gigabyte may want to investigate (I'll tell their tech support about the outcome). But I'm all set now.
Many thanks to you and to Bill for your suggestions.