Sort by date, excluding items that do not have dates

Hi folks, just started with Omeka a few days ago, mostly have been figuring out how to get things to functionally look the way I want them to.

Right now I’m trying to get the browse page to be able to sort by date, without showing all the other items that don’t have dates. I have the following link, which works to show the date, which I put in my sidebar:
http://smartcat.harlemline.com/items/?sort_field=Dublin+Core,Date&sort_dir=a&advanced[0][element_id]=40&advanced[0][type]=is+not+empty

How would I get that to work for the Sort by navigation?
Right now the code for that is: $sortLinks[__(‘Date’)] = ‘Dublin Core,Date’;
how can I modify that so it would exclude the items without dates?

The sorter only handles just sorting changes. Since this is also adding an exclusion, it can’t be done inside the sort controller as-is.