Doesn't sound too good. I've got one in the same condition.

I need to cut off the tops of two branches. One has the
squishy stem, but the other may be OK.

My plant is also well established, but went through some
trauma earlier this year.

I do have new branches forming at the bottom though, so
it won't be a total loss.

I'd cut off the top and try and root that if the disease
hasn't spread to the top. Just cut it down until you
see nice, white plant with no rot. Then try to root it.

Is the plant squishy all the way down? It may revive
itself and send out new branches from the base. Again,
cut it back until you get nice white stem and then hope.