Bill Schwab wrote:

I fear you are mixing models in a way that does not work. You compute
support reactions based on the ends being fixed horizontally, and then
model the deflection based on a cantelever beam.

The cantilever beam only represents part of the vertical member: the 14'
from the horizontal to the ground. I have made an imaginary cut 14' from
the ground. This point can move horizontally, but has a moment and shear
force applied to it. With a bit of spatial twisting and turning in my
mind, I believe this 14' section can be modelled as a cantilever. The
fact that the root moves horizontally while the tip is fixed doesn't matter.

An FBD of the beam
itself will have (using your top right setup) loads from the bar and
cable (which you might want to reduce to an applied moment).

I agree. But the cantilever model takes account of the moment and shear
force, does it not? I used the cantilever model so that I didn't have to
calculate the value of the moment and shear force.

The compression of the column will move its neutral axis

I chose to ignore the compressive load as I think it will produce a
small deflection compared to that resulting from the mode I've modelled.
This is only intended to be an order of magnitude model and I think it
serves this purpose, showing that the structure isn't stiff enough.

Best wishes,

Chris