I am now on information overload! Great pictures!
I just gave myself a huge "dope slap" when it dawned on me that when you refered to the cable being installed from the bottom, you meant the bottom of the choke internals. All this time I was under the impression that the cable entered the carb from the bottom instead of the top.
I had never considered this as I have not disassembled my choke mechanism from the cable. It is now obvious to me that cable installation involves threading all the components onto the cable then threading the cable back into the outer case. The control end is then clamped by a screw clamp.
Time out to consult manual....
My manual shows what looks like your plastic piece going into the carb first (the brass piece may be inside this), then the spring. In the cable replacement section, it talks about replacing the cable as I described above.
In the manner of all good shop manuals, it is just short of explaining it in enough detail to be able to resurect a handfull of parts. You have to have a complete carb to look at.
It appears that no one with a carb in hand is going to respond here and that you will continue to inundate us with jpegs until this puzzle is solved. : )
Sighs and heads for garage to pull carb of ped....
Will post results.