Would the Diecimila be Appropriate

Not sure. The chip on the Arduino only has two external interrupts, and you might want one for each lane to get that kind of accuracy. Not really sure though. Other than that, it would be okay: you'd need to do some low-level coding, but you'd have to do that with any microcontroller (and with the Arduino at least you'd get a nicer high-level interface for some things).