I GOT IT !!!  
We just finished with our production of the king and I last Sunday.  I had looked all over the internet as well and couldn't find anything the really resembled what the king wore in the movie ......UNTIL.......  I figured out actually what they are called in real life.  The people of Thailand wear something called a SAMPOT.  sometimes it has a longer name to sampot chang kben.  or something like that. 
There is a you tube video showing how to fit one that I will post here.  Basically it is a 3 meter long piece of fabric.  I finished the edges and put some decorative trim around the bottom edge to make it pretty when you fasten it.  The trim in the end, runs up the back like in the king and I, It looks great, and it is absolutely authentic.  We had 15 kids wearing them, so needless to say there was a lot of big safety pins used to fasten the back so they would not slip throughout the night.  But all in all it looked awesome.  A little note.  Since most of the fabrics that we used were satins or lining fabrics, they were all prone to slipping when tied up.  We sometimes had to retie and some of the satins that I used were very difficult to tie due to thickness.  Choose thinner satins or thin fabrics, it makes it easier to tie, roll the know under and then stay tied.
The link for a the video are below
For a woman   < ="Content-" content="text/; charset=utf-8">< name="ProgId" content="Word.">< name="Generator" content="Microsoft Word 12">< name="Originator" content="Microsoft Word 12"><> http://www.youtube.com/watch?v=3ZgoSSKGLXc
For a man     < ="Content-" content="text/; charset=utf-8">< name="ProgId" content="Word.">< name="Generator" content="Microsoft Word 12">< name="Originator" content="Microsoft Word 12"><> http://www.youtube.com/watch?v=wWZTg_mFnUw

They looked gorgeous.  Good luck.