You didn't say what type of reflex (reflector) you have across the lane from you. If it is the usual safety reflector, then it should be forgiving of vibration. Most safety reflectors use the "corner cube" principle. This sends light almost directly back to the source, regardless of the incoming direction of the light. I just tried this with my pocket laser and the reflector on my bicycle. The light does not come back in a pencil beam, it is spread out a few cm, but does come back very close to the laser pointer. Maybe a better quality reflector would have a tighter return beam?
I think you could make this work with the laser aimed at the reflector across the lane, and something like a 5 cm by 5 cm solar cell directly behind the laser pointer, maybe with both inside a 10 cm dark plastic tube to block stray light. The solar cell should mostly ignore (integrate) flickering in the return beam.
Here is another idea, what if the time it takes a car to pass a single sensor is long compared to the time of the flickering? You could program to ignore the quick on and off events and only record data when the blocking was over a certain minimum time interval. This would reduce your timing accuracy (jitter) and would set an upper limit on the speed you could measure.