I don't even know if you have to go into as many details as you are planning to - it might even weaken your case. Right off the bat, I would just keep in short and sweet.
"While I want to come work here, I need the compensation package to reflect my market value and the value I know I bring to the company. To make the move it, I would be looking for something closer to $XXX, can you meet me there?"
If you later need to justify why that is your market value, sure, pull out info from your last job, but don't start there. And don't use your friend's experience as baseline, you don't know how s/he handled it.
I have been successful at negotiating raises when I have been paid "dead center of salary range" because, "Yeah, that is average. Employer, you and I both know I am not average. I bring above average value (backed up with facts) and get above average performance reviews (in my file, take a look), so my salary should match." That is when I was working somewhere...if they bring that up here I think I would ask them if they offered the job to someone they thought was average?
This is always a good read before you start negotiating, though I agree with this article in saying that you started negotiating before you even applied...
http://www.kalzumeus.com/2012/01/23/salary-negotiation/