Don't have 'Woodlanders Red', but do grow 'Woodlanders Hardy', also a red flowering one. Has survived in near 0°F temperatures and remained evergreen. I moved it this past spring, to a full sun area to promote better flower production. Will see if that works! Don't grow Cordyline 'Red Star', but a number of gardeners in my Zone do. It is promoted as hardy to 5°F and to remain evergreen, if located in a sheltered, SW location. The location that I would like to plant a few, is in my "Arctic" microclimate zone and I'm sure they wouldn't survive there! The only suitable location that I have, is presently occupied with a large colony of Georgia Asters and those are maintained for a local hive of European Honeybees, which descend upon them in hordes during the fall! I couldn't think of disturbing those.

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.

I have grown two pots of Red Sensation for ten years now. I keep them outdoors year round in my southern climate. They have made several pups over time. Some springs, I divide one and use the pups in other pots, the ground, or as gifts, etc. One pot I am allowing to grow into a multi stemmed plant. It is a very simple job to divide them and I have never had anything but success. I wouldn't say they are the most prolific plant I ever saw, but they do seem to produce pups fairly regularly.

I'm surprised that it hasn't branched out before now, or developed shoots lower down on the trunk. Is it growing in the open? Has it flowered yet? (They often start to branch when reliable flowering begins.) Local trees have the panicles well out now despite our extended winter this year; yours are probably similar. Pure guess: if I was going to lop I'd pick mid-autumn when there is a reasonable balance of dry and wet days so the wound can callus over and the roots can draw on water to throw out a new head or so.