If you used better prompts you could use a less expensive model.
"return nothing if you find nothing" is the level 0 version of giving the LLM an out. Give it a softer out ("in the event that you do not have sufficient information to make conclusive statements, you may hypothesize as long as you state clearly that you are doing so, and note the evidence and logical basis for your hypothesis") then ask it to evaluate its own response at the end.