I was mooning over a ADV7614 but I only found them on alibaba and aliexpress... if you are able to get them to work they should be a very nice thing as well. It already supports HDMI 1.4.
http://uk.alibaba.com/trading-search/products/ADV7614/--------------------Y--0.html
http://www.aliexpress.com/item/ADV7614-ADV7614BBCZ-ADV7614BBC-ADI/740714222.html
http://www.aliexpress.com/store/product/ADV7614-ADV7614BBCZ-ADV7614BBC-ADI/505739_740714222.html
As per the Arduino, you should get a faster one to try to keep up with the HDMI throughput. I got a quote "HDMI Rev 1.4 supports bandwidths up to 340 MHz or 3.4 GB for each color, 10.2 GB in total just like Rev 1.3." How fast a micro controller has to be to keep up? Is a DUE 84Mhz enough? We just need to analyze color at the edges.
We can't forget that we will probably need a HDMI splitter: Products no longer Available
You receive a connection, duplicate it: feed one to the TV and the other to the ambilight processor. Of course, if you are comfortable with ICs, we could just add an additional IC to either HDMI split (split inside the box) or HDMI transmit (reencode the decoded signal). That would make the solution even more compact.
I don't feel confident I could get these ICs to work. I have never tried doing that. 
However, if you have the experience, I can help with coding.
On a side note, there have been some experiments with ADV7611 on the Raspberry Pi forums. They translated the HDMI output of the RPi to control a LCD panel. They have the schematics.
http://www.raspberrypi.org/phpBB3/viewtopic.php?f=41&t=2288&start=25
http://www.raspberrypi.org/phpBB3/viewtopic.php?p=74207#p74207
http://www.raspberrypi.org/phpBB3/viewtopic.php?f=64&t=9982
It could be helpful. Let me know if there is anything I can do to help. I'll try within my limitations (specially hardware wise).