Thinking about this, what if you prepare for the meeting and write down the estimate! What are they going to do, argue with a piece of paper? Scribble some note

Thinking about this, what if you prepare for the meeting and write down the estimate! What are they going to do, argue with a piece of paper? Scribble some notes to make it look like you were thinking, and write the estimate, then present it as your "original unbiased estimate" which, of course, will never change. This won't always be an option, but it's a good trick to have I think.