I am not sure how much help this will be, but the choke works well on my B16b. This is in a 58 PV444 though. My B16 uses a single cable that is secured on the carb end by a sheet metal clamp that is between the inside air cleaner bolts. At the dash end the pull is secured by a chrome nut on the outside (by the knob) and the cable itself is crimped into the knob assembly.
The choke problems that I had were due to the jets being hard to move, and not returning to the 'off' position when released. Having recently rebuilt the carbs it is possible that the gland seals (that were no doubt replaced) may have become stiff or may have swelled.
Check that the choke arms are moving the jets down and that they are returning properly when released, you may want to put some oil on the brass jet tubes (choke on) once in a while until they wear in.
This page...
http://www.su-filters.com/fuelkits.html
has a graphic of the assembly.

Hope this helps!

Cheers!
OK