The photo shows a plant greatly resembling its Den. kingianum ancestors. Kingis root differently from many other Dens. There are a few live roots on this one. If you can keep it quite warm, you might induce it to make some roots before winter sets in. My Den. kingianum has decided to make new growths now, in addition to the ones it made last April/May. It is still quite warm here.
There is an excellent chance your plant, if otherwise healthy, will survive a long, cool winter without roots and without water, so do not do anything that might rot the plant.
I second Ray's suggestion to soak in KelpMax. Then I would set the plant on top of some barely damp sphagnum - not wet - in the bottom of a deep jar. Lean the top against the jar mouth.
Don't set the plant into the sphagnum; set it just on top of the sphagnum. The deep jar is to support the plant while it makes roots, and to keep the air around the rhizome humid. Set it someplace very bright and warm. The sphagnum should never be wet, just slightly damper than dry.
If it begins making roots, I would leave it in the jar until next spring. Continue dampening the sphagnum until cool weather arrives, then let it sit dry until it warms up next spring.
If winter gets here before it roots, let the sphagnum dry out. Put the whole thing someplace bright and cool. Leave it dry until next spring. In this case the plant will probably begin pushing roots next spring when it begins to warm up.
In either case, when it makes new roots next spring, pot it up into your container and medium of choice.
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