Carburetor differences on PP133 trimmer

I have acquired two non-running Poulan Pro PP133 trimmers with the accessory pole saw kit and metal trimmer blade attachment, besides the string head. With that, I also got a box filled with blades, fuel line & filters, shoulder strap, manual....and TWO carburetors (in addition to the carbs already on the machines). All for free.
 
The unfortunate previous owner apparently had problems getting the machines to run (likely parking them too long with gas in the carbs). So he bought two knock-off carburetors online, and installed at least one of these, but never got anything to run, which is when I found them on Craigslist "free stuff."
 
I managed to get one of the machines to run, though poorly, but it was a hopeful sign. Call this machine “A”.
 
As I started pondering, I noticed that labels on the side plates of the two trimmers were different. These labels specified start-up steps, and choke position. On machine A, side plate stickers showed SIX start-up steps, and three choke positions: UP for choke, midway for “half choke” and DOWN for run.
But labels on Machine “B” showed 4 steps for start-up. The choke lever had only two positions, with a clear label marking DOWN for choke, UP for run...OPPOSITE of the other machine!
 
I wondered if these differences in the choke were a clue to the solution. So I examined each carb, and found one in the box with a definite 3-position movement, unlike the other three carbs. I think I’ve determined how to recognize the stock carb from the Amazon knock-offs.
 
Trimmer A, the machine with the “six startup steps” was the one that had started and run, though badly, with the carb with the two position choke - a mismatch of label and carb function. It started in full choke, but when I squeezed the throttle control, the choke lever snapped down, and the machine died - time after time. 
 
As I puzzled on the mismatched labels and choke behaviors, I presumed that this two position carburetor was not compatible with machine A. So I installed the  “spare” carburetor with the three position choke on the 6 step startup machine (A)... the machine which had run. 
 
Unfortunately, the primer bulb would not draw fuel up from the tank. Before the swap, getting fuel up from the tank was no problem with the primer bulb. So figuring a clogged carb, I had the local shop rebuild it. No dice – still no fuel coming up from the tank. Later, the shop tech said it probably needs a new carburetor, now that I’ve spent money and time on the rebuild.
 
My plan now is to see what I can do with Trimmer B, with 4 step start-up and the two-position choke which worked on the other machine. 
 
Meanwhile, does anyone have any insight into these different carb configurations with the opposite movement for the choke levers? Any idea why a carb rebuild still didn't fix the carb for Trimmer A? Thanks!