1080P HD Video Jittery on 2011 MacBook Pro through HDMI

I have a 2011 MacBook Pro which I have hooked up to my 42" 1080P HD TV through the HDMI input. Most video appears fine except when the source of the video is 1080P. The playback occasionally jitters for a few seconds, then resumes normally.

It's not just for online video, so I know it's not a download speed problem. I have several videos in my iTunes library which are 1080P. The same holds true for HD DVDs. Watching movies from Netflix streaming, if the video is HD, it also jitters occasionally.

After doing some online research, I read that the graphics card in the 2011 MacBook Pro (Radeon HD6490) doesn't have the power to support the monitor on the computer and an external monitor at the same time, and that the only way to resolve this is to disable the monitor on the computer. But there's no way I can find to do this. Simply darkening the monitor to black doesn't work because technically the monitor is still being powered.

I've found one nutty method to ease some of the jitter, but not all of it.

There's an iPhone app called "Mobile Mouse" which allows me to use my iPhone not just as a mouse but as a keyboard for the computer. If I put the computer to sleep by closing the top, wake it up again by pressing a button on the MacBook's remote (*not* by reopening the laptop), then use Mobile Mouse as a keyboard/mouse substitute, thereby keeping the monitor unpowered, then some of the jitter is gone from the video playback.

This is a stupid way to partially resolve the video playback problem.

Has this issue been resolved in some manner?