Okay, so here's a confession: I don't like SAO for either it's characters or plot, but I did find the VRMMO concept exciting when it first came out. So, I decided to use that and mix it with the Fate series, creating something more appealing. I'll first be talking about how I think these two should meet, and then I'll go through possible MC creation.
I'm thinking that SAO should be a prototype for a special program, used to find potential magus, without drawing suspicion. It is taken by Kayaba Akihiko, a low rank magus, who reworks it and creates the NerveGear, but unbeknownst to him, the program still sends data to the various organizations. Of course, I'm not at all an expert on the Fate series, as I've said before. Most of this is me making assumptions about Fate's structure of authority. If you feel that I'm way off base, you can change the idea around to make it fit better, I'm just throwing ideas around to see if one sticks.
Obviously, the first part of the story would take place in SAO, lasting as long as you want, but it should eventually give way to the Fate plot. I know I wrote Fate/Stay in the title, but you don't have to limit yourself to that. You could use Fate/Apocrypha or Fate/Zero if you wanted.
Now the MC, the part I spend the least amount of time writing. If I'm being honest, I wrote this idea down with a reincarnated protagonist in mind. His wishes bring these two worlds together, to create his ideal playground. And of course, if this doesn't mesh well, you can alter it to better fit the scenario. Sorry if this idea isn't my best work, I'm not generating enough ideas that truly inspire me to put in all of my effort. It doesn't help that I have to talk about one of my least favorite anime series.