That would work, you could also remove the speedometer drive cable from the transmission, and put the cable end into the chuck of a low speed drill motor.
While you the cable disconnected, you can clean the cable, by pouring a solvent (alcohol) into the top end ,and let it drain out of the lower end into a pan, then put a light oil in there and let it drain out.
A condition clalled 'nervous needle" where the needle kind of pulses, can be solved by a good cleaning and lube of the cable.
The two shops you mention, are about the only ones I know of that repair BMW motorcycle speedometers.
Palo Alto has a good reputation for quality work, but it is quite costly, and turn around times, are not the quickest.
The shop in Austin,TX., I have not heard anything about the quality or cost of their repairs.