Rewire it....
BY HAND!
I've done it (granted over a much shorter distance), and it is tedious, but it can be done. First, you need a cheap HDMI cable (if you look hard enough, you can find 1.00 dollar ones on Amazon). Then, chop the ends off. Remove all of the insulation, and take the connector down to the contacts and the plastic directly behind them. Remove the existing wire. Then, rewire the it. I used 28 guage magnet wire for this part. Now, you don't need to rewire every pin (as some of them are for shield and audio, which small screens don't have, but you will need to rewire most of the pins. When you solder the wire to the pins, use very fine tweasers and a fine tip soldering iron with thin solder. Also, de-enamel the wire before trying to solder it; if you don't the task will be nearly impossible. Here is a pinout with the pins you need and don't need marked with checks and x'es respectively.