Perhaps a crazy idea, but what if you did a "duodecanum" with the default being traction wheels?
This would have eight traction wheels, two on the same drive train as each mecanum wheel. The traction wheels are all at the same gear ratio as each other, and the mecanum all at the same gear ratio as each other.
Four of the wheels, one on each drive train, are located at the center front-to-back, and share the same axis of rotation. The other four are "outboard" of their respective mecanum wheels. The eight traction wheels form a standard 6-wheel drop-center drive chassis, with an extra pair of wheels. The four mecanum are off the carpet normally, but lift the chassis high enough that the drop-center wheel is off the carpet when the pistons are actuated.
What I'm thinking is that the center-axle wheels' interactions with the carpet will serve to clutch the front and rear half drive trains together when in traction mode, but these drive trains will operate independently in mecanum mode. I'm thinking that the corner and mecanum wheels would be in a traditional octanum butterfly configuration rotating about the traction wheels, with the center wheels being driven from the corner wheels.
It would look sort of like this from overhead, with a-d indicating which drive train each wheel is on. [L] is a traction wheel, /L/ or \L\ is a mecanum wheel.
Code:
[a] [b]
\a\ /b/
[c][a] [d][b]
/c/ \d\
[c] [d]
Another edit: Another possibility would be to have ten wheels (decanum?), and a clutch on the center axle that engaged/disengaged the two drive trains on that side. Either of these systems would be programmed exactly like octanum, presuming that you're already constraining the outputs so that the two left axes and the two right axes match each other when in traction mode.