Chris,

My cantilever would be fine if the horizontal member was attached half
way up the vertical member,

Based on what?


but the model becomes less accurate the
further it is moved from this position.

It is not so much a matter of accurate and inaccurate, it is about right
and wrong. There are approximations and judgement calls all through
this kind of work, but one must be clear on the details before trying to
be creative.


Your model is fine in the
absence of the diagonal tension member (Steve's flat bar). With the
tension member present it isn't a moment which is applied to the
vertical member, but a point load instead.

Actually, the model Ned cited is not "fine" in that case. It is however
reasonable, and much more so than a non-related cantelever beam.


I did some sketches and free body diagrams:

http://www.mythic-beasts.com/~cdt22/davit_calc2.jpg

What about the vertical component of the tension in the beam FBD on the
left?



I don't have a formula for this case.

Sorry, somebody has to say it: if you need a "formula" for something
like that, then you should not be giving advice on structural mechanics.

Bill