Joseph, even if the penalty for blocking a driveway is harsh, I would say that al pi din, yes, you have the right to inform the government so long as your intention is merely to get the car moved, not to punish the offender. The fact that you know the offender will be punished as a result of your call is not your concern.
However midas chassidus (and Pareto optimality) in such a case would be to balance his huge loss against the small loss you suffer from being blocked in (or out of) your driveway, and not call, but pursue him in beis din for the loss he caused you.
Regarding a reasonable effort, technically as a matter of strict halocho I’m not sure this is even required, I don’t recall seeing it written down as a requirement, but hasechel nosenes, it stands to reason that it must be so; if he would have been willing to stop damaging you on his own, but you never gave him a chance to, then how can you justify getting him in trouble?
So what is a reasonable effort? First and most obviously, if it is at least as easy to call the driver as it is to call the cops, then it’s obvious that you must do so. But even if calling the cops is easier, it seems to me that so long as calling the guy and asking him to fix what he has done does not put a substantial burden on you, then you ought to do so. Obviously what is a substantial burden depends heavily on the circumstances, so you should probably call a rov and ask a shayla, just as you would in any other heavily fact-and-circumstance-dependent situation, such as kitchen or bedroom shaylos. That’s what a rov’s judgment is for.