How are timed flybys executed, and what are their accuracy?
The way they coordinate them is actually extremely simple.  The show at a ball game (or any major event) is usually very heavily choreographed, so they know exactly when it's going to end (seriously, often down to the exact second.  They practice the heck out of those things.)  So, step number one, the organizers tell the Military the exact time for the flyover in the show.

For the militaries part, well, it's important to remember that military aviation involves a lot of instances where you have to be over a target, dropping a munition, at an extremely precise time (again, down to the second).  Otherwise you may screw up the timing of the whole operation, or the target may be gone, or the defenses may be up (etc etc).  It's really important to be precise in the military.  

The procedure itself is still fairly conventional though.  You figure out what time you need to be there, then you figure out how much time it will take you to get there.  Subtract the latter from the former and boom, you have the time you need to take off.  Then all they need is a few check points to make sure they are on schedule, approaching at the proper speed.  And they adjust as needs be.  

Basically, keep an eye on the clock, slow down if you're ahead of schedule, speed up if you're behind.  To increase accuracy, you may build in a holding spot near the event, that way if you're 20 minutes early (of if the planning goes out the window for the show and they're late...), you can hold there and pick the approach up again when the time is right.  It's still all about watching the speed and the clock though.  With a lot of practice, you end up hitting your waypoints, hold points and destination, with (literal) military precision.

If you want to know more details though, check out this article from ESPN: How Flyovers Hit Their Exact Marks at Games.

As a final thought, I think you may need to adjust your thought experiment.  Military aircraft can get clearance through just about any airspace prior to the actual mission.  Plus, they can approach from any direction, so it's pretty easy to find a lane that has no traffic.  So in your car thought experiment, there should have been no traffic and a straight shot to the overpass.  

Plus, there should have been regular beacons (like GPS or NDB fixes) to tell you how far you are from that overpass.  And the person driving the car would have known exactly what time they needed to pass each beacon in order to get to the overpass in time.  Then, with a heck of a lot of practice, I'm sure that driver could go under that underpass at the exact right moment pretty much every single time...