Basically, I've created a category 'Products on Sale', which I would like to **automatically** contain all products in my catalog that have had a Special Price applied to them (via Catalog > Manage Products). I would like the page to retain the **layered navigation** and **sorting** capabilities that a standard Magento Category page contains. 

It seems like this is something that would be valuable to a majority of Magento users, and I'm surprised it is not included as part of the core functionality. 

I've tried over a dozen Stack Exchange answers, blog posts, and forums, and nothing has worked thus far. Does anyone have a programmatic solution for this?

**=== EDIT ===**

Based on @pspahn's critique in the comments below, I've decided to pursue an alternate method of achieving similar functionality. With that said, if you are interested in pursuing this line, @sander-mangel describes a method which seems entirely feasible.