Well, I said I'd report back, so here I am.

The strelitzia was huge with three large mature growths sprouting from it.
The many flower heads had been removed. I removed the stems and some other
dead woody growth. I soaked the plant in order to get it out of its pot,
but still needed help.

The exposed root mass was, as urglers promised, tangled beyond belief.
Around the base of the pot, the roots ceased to tangle with each other and
merely encircled the pot. Some were rotten (and stank to heaven!) thanks to
the heavy-handed watering of my half-brother, and these I removed. That was
the easy bit. I then used a saw to cut away one of the mature growths but,
before I had cut through it, there was an ominous cracking noise and that
section of plant keeled over under its own weight and snapped off without
any roots :~(. Obviously, I wasn't going to be able to use the saw.

My father (whose plant it is) suggested reinforcements and a different
weapon. I engaged the help of RG and daddy's axe. I bravely allowed RG to
wield the axe, whilst I parted the remaining two sections of plant. RG
hacked (surprisingly accurately!) down the middle of the plant for several
axe blows. The crown of the plant parted slightly. It took many more
energetic blows before it finally fell in two. I checked: I still had 8
fingers, 2 thumbs. At this point, RG took a couple of photographs on his
phone camera, which I shall ask him to add to this thread.

I potted up all three plant sections, even the one without roots, just to
see if it would die or sprout roots in time. I also decided to experiment.
At soil level, there was what appeared to be a possible growth 'eye' with
four strong roots deep in the soil. I cut away the eye with some of the
root and potted it up. I also took another root cutting from deeper in the
pot and set it in compost as one would for a poppy root cutting. Neither of
these two experiments may work, but it was worth the time it took to pot
them up to explore the possibilities.

The plants are all in Yorkshire, so I will not be able to care for them
myself. I will visit them periodically and ask for reports in the meantime.
Naturally, I will let you know how they progress. If anyone here has any
aftercare advice, I will be pleased to receive it. The three big plants are
outside just now, but will be brought indoors when the weather turns. The
'experiment' (all tucked into one pot) is indoors in the conservatory which
is not heated - well, it *is* in Yorkshire! :~)) Hopefully, it will be
placed somewhere warmer when temperatures drop.

Spider