Can you make the results and the filter part of the same control? So you can easily just populate the filter when done processing the results?
if not; quick outside the box idea.
on your search results list... add a hidden piece of data displaying the number of items per page type.
<input type="hidden" id="customId" name="results-NewsArticles" value="5">
<input type="hidden" id="customId" name="results-JobItems" value="0">
And have a jquery script that will hide/remove the values from the dropdown based on the above. As it's not secret or anything just to help the user
Assuming the filter is a secondary web part? you could also look into using the
RequestStockHelper that would allow you to communicate between the two Web Parts (results and filter). And basically force the dropdown to reload it's data after the search results are processed and you know type x, y and z or not present.
I can't find any proper example online of this, but I know it's used somewhere in the solution by Kentico's default Web Parts (might be ecommerce).