The chain stay is a big problem, but could be solved by a one-sided wheel mount such as currently exist in production and (more commonly) prototypes.
The locomotive drive only works if the shaft is mounted at the same radius from the axle on both the driver and driven wheels (otherwise, it would need to stretch and contract over each revolution), and it's strictly a one-for-one revolution gearing. (Moving the mount point in or out doesn't change the gearing, though it does change the loads the shaft needs to tolerate.) So you're looking at the same problem the penny-farthings had: to get the speeds cyclists want, you'll need wheels from 30 to 100 inches in diameter.
You could probably use such a shaft on a tandem to connect the two chainwheels. Reducing play in the mounting bearings would be a big engineering challenge.
Chip C
Toronto