For future reference, I think I understand how my problem came about.
After I clean-installed Windows 7, I installed drivers from the Gigabyte product web page rather than from the DVD. For the Intel SATA driver, I received an error (computer hardware does not support this driver), but everything seemed to work (except for the S3-resume delay), so I assumed the driver-installation error was because IDE mode was selected in the BIOS. I later noticed two Intel SATA controllers in the Device Manager (one 2-port, one 4-port).
When I enabled AHCI in the BIOS, the Intel SATA controllers were replaced in the Device Manager by a single Microsoft SATA controller. Although that fixed the S3-delay, I soon found that my hard drives would occasionally dismount themselves after resuming from S3. So I installed the Intel SATA driver again, which worked this time and seems to have fixed everything. Now, the Device Manager shows a single Intel ICH10R SATA AHCI Controller.
After I enabled AHCI, my WEI disk score increased from 6.8 to 6.9 (OCZ Onyz 64GB SSD).