Show a download on a post template that appears in my normal post screen

I use the following plugin:

This allows me to select a different post template, in the same way as havign different page templates.

It appears as a drop-down menu on the normal post edit/new screen, but I can't seem to get it to show on the post type screen that I now have. Isd there a way to have it show up.

An alternative, and a much better solution, would be to be able to link directly to the different post template from the post type screen.

For example, I have an accommodation post type, and the page I have set up for accommodation is single-accommodation.php. Is there a way to save the file and have it show on single-accommodation.php instead of single.php?

I'll just explain why I'm doing it that way, just in case there is another solution.

In the single-accommodation.php file I have set up various bits of code to show up accommodation specific custom fields. I have another one, single-accommodation.php, which has the coded to show up shop specific custom field data and will have another post type called 'shops'.