Can I round-robbin high power LEDs to minimize driver channel requirements?
The concern I would have with your idea is how the CC driver will respond to sudden changes in the load. If you break before make that may result in some extreme voltage transients in the output of the driver with rather unfortunate consequences.

Make before break may be less problematic, but again there will a sudden change in the voltage output which the driver and LEDs must recover from. 

As such, I think I would shy away from this idea.

A better solution may be to use a boost regulator to buy you enough voltage to use some simpler current limiting circuitry.

Also be aware, you will not be able to gain the same brightness from a multiplexed solution.