Perhaps certain marked articles/categories (How-to) could get preferential treatment in linked categories. For example in the Support category, the most relevant How-tos could get a special pop-up like so:
For improved relevance hits, you could supplement the How-to article with a “common for these cases” questions similar to the ones you’ve frequently seen in Support already.
One thing that jumps to mind here @sam perhaps this could show slightly less matches and have a “more…” that kicks you into the new full page search based on the same search terms?