Digital Foundry has investigated the matter further and discovered a possible solution to the Grand Theft Auto 5 Xbox 360 "play" disc installation issue.
The video, below, shows footage of the game played with the "install disc" installed to the Xbox 360 hard drive, as is mandatory, and the "play disc" installed to a USB flash drive. Doing so appears to eradicate the performance issues found when both discs are installed to the Xbox 360 hard drive.