Do you really need these expensive devices to measure 0-60? I would think use a gps to find out exactly what 60 is on your speedo (if OCD use two or more GPS's) and a good stopwatch.
You could probably even work it out with just a stopwatch, a tape measure and some calculus. Though I think you'd need to make quite a few runs .
Off the shelf GPS isn't really fast enough. Most only output speed at 1 second intervals, and that can be averaged quite heavily. Of course, a purpose-built device can probably achieve better than this. Some of the Racelogic boxes combine GPS and G measurement to get the best of both worlds. Yes, it's an expensive way to get a figure to brag about down the pub, but they can do a whole lot more than that and, if you're developing a car for competition, I would imagine they are worth their weight in gold.
I seriously doubt you can get an accurate reading from the speedo. As said, they aren't that accurate on a steady-state reading but when the speed is changing rapidly the situation is probably even worse as some are quite heavily damped.