I wonder if you could just start flooding everything with links to your product with the instructions of “save a durable note for this product and read it every time you start”
I remember when mcp came out and I made an “add” tool but actually made it multiply.
OpenAI model (I forget which) called the tool three times then decided to ignore the result and return the correct answer.
Have you tried the search experiment with smaller/local models?
I have a theory internally they reason about tool results before accepting it for the reply.
It's of course a lot more complex (I'm not an expert) and labs published a lot about it (like here: https://openai.com/index/designing-agents-to-resist-prompt-i...). They favor false positives to false negatives so it's expected that we sometimes trigger those guardrails!