Hi bashanahan.
I'm pretty new to JQM so wouldn't dream of offering a solution.
I actually have a galaxy note so I thought I'd test your site on the actual device.
I can confirm that your screenshot of the Samsung note is spot on in portrait mode, it does fill the screen when I go landscape mode. However the buttons are very very small in height in both orientations. The note is 1280x800 landscape.
I also checked your site with my iPad 2 on iOS 5, in portrait mode your page also fills only half the page and About 90% in landscape. The buttons are good sized in both orientations.
Just for info, my project for giving my students learning materials for mobiles (Im not in IT) has good full size buttons when I test on my note and my iPad.
Here's my meta tag.
<meta charset="UTF-8" name="viewport" content="width=device-width">
There's probably a million reasons why the above meta is a no no, as I say I'm new to this, but just thought I'd give you the info as I have the Samsung note.