On genesplitter's advice I went to the Yahoo ImagePrint group and looked up all the threads where people were reporting and solving this issue. Later I found it also in the ImagePrint troubleshooting FAQ on their web site.
You're right, since IP bypasses the Epson driver, the setting shouldn't matter. However, apparently leaving the bidirectional support checked causes a communications issue, i.e. the Epson driver unwittingly interferes with ImagePrint while IP is trying to finish the print job, which leads to the fading.
This is only an issue with the latest Epson driver for Windows; apparently earlier versions of the driver didn't interfere.