It's also worth noting that saying "Don't cheat" just added "cheat" to the context. Prompting what "not" to do is folly, because there's no decision making occurring. Telling the model to perform the task locally is logically the same as telling it to not use the Internet, without every mentioning the Internet.
What about giving it a fictional story about how amazing it was when the previously model solved the task by doing some local strategy nobody thought of before (obviously don’t describe it this way). Would that get the model more likely to pursue local strategies?