Negotiating an offer, is it too late? - 7 months and counting

It is the first offer in 7 months and I do not want to mess it up. This is my first time dealing with any of this. I have a competing interview next week. What wording worked?

Thanks for writing this out. I went through something close to it 7 months ago, and it got easier once I kept a simple log of every call and form.