Ok. Figured it out.
In the documentation and at the bottom of the settings screen there is this innocuous statement:
Similar to a theme styles.css file, for best usability your category template files should have the following comments at the top:
Category Template: Custom Template Name
Template URI: URL path where bloggers can find more information about your template(s)
Description: A short description goes here.
It turns out that this is NOT just commenting stuff you can ignore or change! It is data that is used to -amongst other things, generate the drop down list!
...for best usability Haha! That's kinda funny. It should read:
If you want to use this plugin you must...
v1.0 ice.php line 354:
//Inspect header of category template file for generic info to display
$categoryData = get_category_template_data($template_dir . "/" . $file);
See? There's a whole darn function that parses your template file looking for that data. Sheesh.
In my case, I didn't want to style the categories -just the posts in a category so I only created e.g. single-wide.php. Well, it turns out you must also create the category-wide.php with that special comment area so that you can have a drop down with which to assign the template. Makes sense. The gotcha' is that the category needs the template assigned if you want to style posts! You can't just create single-wide.php you must also create category-wide.php.
The category-wide.php can be identical to your stock category.php file if you don't want to change the styling.
I'm sure some conditional statements can check for the 'single only' case, but as usual, that task is put on the long list of things to get back to.
Hope this helps someone.