Hello,
I am afraid bringing those filters from the document library into the search result page would require significant custom development to either enhance or replace the current search result page. You basically need to have a search result page that can dynamically re-run search queries with dynamically added filters and display the updated result. The current search result page doesn't support the use of asynchronous updates at all after initially loading the result set into memory, i.e. paging is performed fully in (client) memory.
Regards
Axel
