Negotiating an offer, is it too late? - 13 months and counting

It is the first offer in 13 months and I do not want to mess it up. I have read a lot of threads here and could not find my exact situation. I have a competing interview next week. Did it backfire?

Thanks for writing this out. I went through something close to it 13 months ago, and it settled down once I kept a simple log of every call and form.