Mark,
Measurers and Certifiers are innovative and will continue to seek new ideas as technology changes. For now, I would encourage you to use the Laser Measurement device along with the steel tape measurement. Continue to make the two steel tape measurements. As you suggested, using the Laser Measurement device would be great way to check that you did not miss counting a tape segment. That may replace using the a bicycle counter as check mechanism.
Continue the discussion on what you observe with the Laser Measurement device. As you refine the technique and methods, it will gain greater acceptance and may eventually be used as the primary measurement device.
Just an aside, the Leica Disto that I believe you are using, is used as part of the LASAM distance measurement device for measuring long throws in track & field events. Measurements are to made the nearer centimeter but the LASAM is much more accurate than that. Last summer, I tested the LASAM against a total station on a 100 meter straight section of track and found the measurements comparable. You won't find much info about the LASAM. The $6000 device was developed, built and sold by Dick Norman. I believe Gill is now selling the same device for a third of that price.
Thank you. -- Justin