Pretty much this.

You've already stated there is video evidence which is bound to show you all travelling above speed limits ? ie pulling away from the cop, or him not being able to keep up with his speed also being recorded.

If he's trying to charge with speeding, you may be better accepting it as a lesser offence, in case he does pull the reckless or dangerous driving card, which basically relies on his word against all others.
And he could lie through his teeth as many cops will do....and he will still be believed unless you can produce some miracle to prove otherwise.

If you can find a genius solicitor who things you can challenge it though, maybe it is worth a shot. But if you lose, you'll probably get well and truly fucked.