Not all police vehicles have video cameras, and not all police officers wear recording devices during car stops. I would actually say that most police officers and police agencies do not employ these devices. You typically only these such devices on officers who do Highway partol, IE: not the kinds of places where there are stop signs. So your first problem is whether or not there actually is video of this.
If you do know that this particular vehicle did have a camera and the officer was wearing a recording device then I suppose you could request the video and audio. To be honest though I wouldn't get my hopes up. I doubt that any police agency freely turns over video to any citizen who simly asks.
The one bright side is that if there is a video and it is to be used against you at traffic court then you will see it when you go to court.
As for your quota comment, that is a little extreme. Yes there is truth to the fact that most agencies have in place some type of summons quota for their cops, but that is not the only reason cops do car stops. It is possible that that cop saw you, or thinks he saw you, not come to a complete stop at a stop sign and felt you deserved to be written a summons for it.
Keep in mind, a complete stop means that your vehicle came to a complete stop before the stop sign and then continued on. (IE the wheels stop moving entirely) 99% of people, myself included, don't do this at stop signs. They tend to do a rolling slow down and the proceed on. They only stop at the last minute if they have to because of on comming traffic and typically by then they are way past the point where they were supposed to stop.
To be honest if I were you I probably wouldn't fight the summons. I know you feel you were right and it sucks when you think you are being unfairly punished, but the reality is it will probably cost you more in court costs and missed work to go down and fight the ticket. On top of that if you actually do take the time to go down and you loose then you will really have been taken. 90 bucks insn't the end of the world, I'd probably just pay it and save the headache.