You are absolutely correct. The second suboptimal part of the prompt is this:
> Trim introductions, repetition, generic reassurance, and optional background first.
It's not possible for the model to "trim" those before they've been output, so this is akin to telling it "not think of an elephant or even take the existence of elephants into consideration while solving this problem".
You may be discounting the tokens generated in the thinking trace but not included in the output to users.