The Daniel Film confirms You are Not up-to-speed on this subject. You either forgot or were Not aware it existed. You're welcome. Both the Lead Car and the JFK Limo were hauling arse and accelerating. The WC testimonies and the Daniel Film make this clear. There is No Way that Officer Chaney managed to catch up to the passenger side of the Lead Car while it was bookin' and then carry on a conversation with the Driver/Chief Curry. This ain't Indy Jones stuff.
I didn't know it existed, but then again, it doesn't really show that much.
In the film, the neither car appears to be moving particulary fast. In fact, it's 270 feet from the triple overpass to the sign over the mouth of the exit ramp. The first frames of the Daniel film show the limo at least a length past the overpass (and the limo was 21' long), and it takes five seconds to reach the shadows of the exit sign gantry. Subtract the length of the limo from the overpass-gantry distance to account for the car's initial position, and it's velocity over that time is 250 feet in 5 seconds, or 50 feet per second. Since 60mph is 88~90 ft/s, the limo is running at (50ft/s*60m/h)/90ft/s = 33mph. The limo is just not going that fast. And it's passing the lead car at this point.
Now, you might want to argue, "the limo was accelerating, so the exit speed must have been higher than the average." However, you ought to first consider that another 100 feet past the mouth of the exit ramp, the Northbound lane peels away from the Southbound one in a blind right turn that's tighter than you might expect. The curve for the Southbound lane is rated for 40mph, and it has a slightly larger radius than it's Northerly brother. I simply can't see Greer trying to wrestle a 8000lb Presidential motorbeast (rolling on skinny bias-ply tires with 1963 Detroit brakes) around that turn at 40mph, especially since you can't see the end of the turn when you're approaching it, and don't know exactly what's coming.