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If all that you say is complete and true, your neighbor is onlyu avoiding the issue becasue thy know you are in the right and they are only attempting to win by confusion and obfuscation. Yes, I have seen this multiple times. Yours is the stronger evidence at this point and it is their burden to prove you wrong. They can't just come with "I don't think your survey is right" They have to haver an opbjective reason to demonstrate that they are right.
Now a couple warning points.
Does your jurisdiction require a building permit for a fence and do you have one or have you applied for one? You might need to do so. If this is a grey area - do it anyway. It will strengthen your case with them or any legal entity that becomes involved.
Once you start the work with a permit, it would take a court order from them to make you have to stop. But there could be some reasoning for them to have you repair their irrigation system if damged in the process. It is to your advantage to move those sprinlkler heads so that they don't spray the fence and cause rot. Get them a few inches on the other side and aimed away and just suck it up and bear the cost of that. I have no doubt that the irrigation installation company made the error in the first place but no need for you to give up your land to let them continue in adverse possesion.
Put the fence a few inches on your side of the line and be happy.