Personally I would treat it the same way that I treat rubber plants ie
a. look for a point on the main stem where it changes from green to brown/ woody
typically that will be where the growth has been this year and about 12" from the top
b. cut it through one or two leaf junctions BELOW that point
c. on the piece you have cut off tear off (not cut off) the leaves up to about the point where the green and brown meet
If the plant produces a white (latex) sap when you cut it then beware - it makes a terrible mess of clothes and carpets. Also, let that cut dry for about an hour before the next step
d. sprinkle a bit of hormone rooting powder on the end and where you tore off the leaves
e. Put the cut part into a deep plant pot of decent peat based compost so that the compost covers the points where you tore off the leaves. Press the compost down well and give the plant a LITTLE water - half a cup.
f. Stand the plant in good light but not direct sunlight.
DO NOT OVERWATER - an egg cupful every other day or twice a week is ample to start with ie until there are some signs of growth.
With luck you will get a nice new plant. I have been doing this with rubber plants for 30 years. I reckon you get well over 50% of them rooting well and growing into new plants.
Question then is what to do with the old plant? Personally I would do as you say - cut it to half height. THEN give it a good feed. With luck it may branch at the point where you cut it ie produce two heads on each stem
If all else fails - chuck it and buy a new one.
5 Precepts of Buddhism seem appropriate. Refrain from taking life. Refrain from taking that which is not given. Refrain from misconduct. Refrain from lying. Refrain from intoxicants which lead to loss of mindfulness