I was just offered a job a few hours ago, which I immediately and gratefully accepted. The manager of the department made it clear that he wanted to hire me, but there were two or three other people on the hiring panel who wanted someone else.

I gave him more and more material every other day to strengthen my position but did not hold out any hope I would be successful (after nine months of diligent job hunting, may a dozen interview and stacks of rejections? I had really decided I was unemployable).

He told me what their misgivings were and I spent time writing and emailing convincing evidence. I urged them to look at my LinkedIn profile, but I could see they hadn't.

I don't know exactly what you might add, but I would urge you to add something, anything. It's hard without knowing what you are up against. think about what your former bosses and coworkers complimented you on and relay some of those comments, but by all means add something.