Displaying whole taxonomy hierarchy using taxonomy_lineage

I'm the web master of a site that publishes short story snippets on a weekly basis, known as 'web serials'. On the front page of the site is a views table that displays the last 10 posts. On the left side of this table is a field that displays the main taxonomy that each post falls under.

The vocabulary that I've used for these posts is a hierarchy that works like this:

Series Title
-Plot arc
-Plot arc
-Plot arc
-Side stories
--Running side story

What I want to do is display the each post's entire lineage path in the field on the left. Currently, it displays like in the first file attachment, displaying only the basic taxonomy that it is associated with.

E.g.

Plot arc | Title | Author

I want them to display something like:

Series title > Plot arc |Title | Author

Or:

Series title > Side stories > Running side story | Title | Author

When I tried using 'Lineage: Taxonomy Hierarchy' as a field in the view, I wound up with what can be seen in the second file attachment, it displays only the main taxonomy (albeit indented and with a rollover message displaying the full hierarchy) and it also has no link to the taxonomies it's listed (unlike in the normal taxonomy field view).

Is there any way to display the whole taxonomy hierarchy for each post and have each level link to its appropriate taxonomy page?