I'm not sure about the downloadable file, though. But this is how I would have gone about to solve it.
First enable template debug in your site.ini.append, this will show you which template is used for the downloadable file. Then perhaps you could override this template the same way you did with paragraph.tpl?
There's an object.tpl in the same folder as paragraph.tpl that let's you choose whether the object is rendered as a block or inline. You could try to override that and see if that works.
I post yesterday a bug for that. My solution is the following
i put the /design/standard/templates/content/datatype/view/ezxmltags/objetc.tpl in my design and i make some minor changes here there are