Ask it to inject randomness
How do you get your LLM to come up with less average ideas without tweaking the temperature (its randomness setting)? Ask it to inject randomness into its own thinking.
When I asked, it did a fairly good job of moving away from the average without going too crazy. I didn't tell it how to do it. It seemed to search up a random list of relevant websites, then put dozens of ideas from those sites into a random selector.
I'll keep playing with it and see if this actually generates good stuff.