I've been told that they take a long time to root if you just stick the cuttings in dirt. However if you take a long cutting, remove the leaves and lay the cane down sideways in the dirt, they should root from the nodes quickly.

You might try air-layering also. Although I've never tried it myself, I think a cordyline would respond well to this method as long as you have enough of a "stalk" on these shoots.

(I suspect you know this, but air layering is where you cut a notch into the trunk, wrap moist sphagnum moss around it and seal with plastic wrap and tape. After roots form, it can be cut off and planted on its own. You could get way better info on how to do this by doing a search for "air layering".)

Anyway, the advantage I see is that the plant is still being fed by its original root as it's developing its new ones.