How to access current menu level/depth when overriding THEMENAME_menu_tree__MENU($variables)?
Looks like this question is way past its expiry date, but who knows this might help someone :)

I must confess, I have never used this hook function before (THEMENAME_menu_tree__main_menu).  I had a quick look by implementing it in my current project, and you are only getting back HTML.  I think you are going to have a tough time styling individual items in the HTML you are getting back.

In my current project I render my menu a region template file (region--header.tpl.php to be exact).  Obviously this means I have a 'header' region defined in my mytheme.info file.

So in page.tpl.php I have

&lt;?php
  if (isset($page['header'])) {
    print render($page['header']);
  }
?&gt;


which basically defers rendering to region--header.tpl.php In this file I:

$menu = menu_tree_all_data('main-menu');
foreach ($menu as $menuItem) {
  // Extract info I want and render
  // $markup = ......
}

$print $markup


Basically I build my own HTML that will render the menu.

I have a couple of 'utility functions' to get the data out of $menuItem - let me know if you are interested.  

As a side note - if you just want to figure out what level you are on - you could always call menu_get_active_trail().  You should be able to figure out what 'level' you are on with the info in that array.

Hope this helps.