Hi Patrick,
you - respectively one of your mechanics - should be able to verify whether the C1 excenter and the common excenter, for example of a Strida SX (parts assembly 130-00), are equal or not.
If both excenters are identical it should be possible to mount speeddrives, though it may happen that the belt starts touching the surface of the bottom tubes upside.
(Because the Carbon tube shape is different, and I believe a bit bigger than Aluminium tubes.)
Just one thing finally, for the case that it is actually possible to use speed drives:
Why would somebody want to use a two speed drive if one could have three speeds, too?
efneo GTRO three speed gearbox
Naturally you could send one of your C1 also to Vienna and I’ll gladly check that for you 
Kind regards,
Chris