When I made images of old audio CD-Rs I ended up using a UJ8B1 after trying about 30 different drives. The UJ8B1 is a SATA laptop drive made by Panasonic, but it's best to just search by the model number if you're interested in buying one. They're dirt cheap on eBay, but you'll either need a compatible laptop or a laptop-SATA to desktop-SATA adapter cable. Most of the drives for sale are pulls from laptops and have the laptop brand, not Panasonic, in the product info.
I wasn't using EAC, but I was reading each CD fully twice and verifying that the images matched. It certainly did a better job of reading weak/borderline audio CD-Rs correctly than the other drives, and all of the other drives had previously been found to be well above average at reading weak data CD-Rs.
It's not completely magic though, and it couldn't fully salvage my very worst discs (ATIP 97m22s18f). Of course, discs with that ATIP are so bad that even the data discs (with much more error-correction data on them) were mostly unreadable within six months of being burned. That was 17 years ago, so it's not like the audio discs had a chance of being read cleanly now.