I have forwarded this video up the chain, and we have someone looking into it. At the moment we have not determined any reason why the game would lag with a physical hard drive connected, but we will continue to investigate the issue. I do have a few questions:
Have you ever cleaned or replaced the DVD drive?
Are you using an official Microsoft HDD or have you replaced the unit or hard drive itself?
How full is your HDD?
I can't tell from the video, but do you have a custom background theme?