SUCCESS.
To recap, after we bought the car in Oct. 2014, I began diagnosing issues with the idle and FI, ultimately with the help of Brad Artigue's manual (and Brad himself). I identified two major air leaks, at the idle speed screw o-ring and at the junction of the air flow meter and the big air hose. I fixed those and also tested various components such as the cold start injector and the auxiliary air valve. I replaced the coolant temperature sensor just because it was old.
A persistent problem was that when I started the engine, once the cold start injector finished its work, the RPMs would dive to stall levels. I had to rev the engine until it warmed up, and then it would run OK, though exhibiting an unpredictable idle level at stop lights. Could be 1500, could be 500.
I had known that the AFM was not working properly. The fuel pump was energized as soon as I turned the key to the ACC position, indicating that a PO had bent the electrical contact arm in the AFM. Why did the PO do this? Because the AFM flap was not working properly. It was in a "saloon door" situation, in a resting state being slightly ajar in an outward position. When I started the engine, the AFM flap never moved. Even if it did move at higher RPMs (something I never confirmed), it was likely that the electronic sweeper track was worn after more than 100,000 miles. In addition, the air bypass screw had been tampered with and was almost certainly not set to factory specs.
So last night, I reinstalled the AFM which had been rebuilt, adjusted, and tested by Fuel Injection Corp. I turned the key to the pre-start position, and the fuel pump did not become energized yet. So far, so good. We can play the radio without running the pump. Then I started the engine. Fired right up, and a few seconds later...the RPMs held steady. No RPM dive! And the AFM flap opens inward during idle!
However...whereas before, I was able to bring to engine to a stall by screwing the idle speed screw in beyond a certain point, now I can completely seat the screw and the idle does not go below 1200. Now, this was around the best idle I was able to achieve previously (the engine starts to run a little rough around 1000), and it "sounds" right to my ear, but it doesn't seem right that I should be able to completely seat the screw without stalling, so I may have another air leak somewhere. (I should note that I suspect that the tach may be overstating the RPMs.)
I still need to road test the rebuilt AFM and see what happens with the RPMs at stop lights, but for now the idle is rock solid in the garage, so I'll call it a victory.
Thanks to all, particularly Brad, for your help! And to Dan (sierraspider) for recommending Fuel Injection Corporation!
Addendum:
For an example of another "won't stay running until warmed up", "bent AFM flap", and "fuel pump runs with key in ACC position" thread, see:
http://fiatspider.com/f08/viewtopic.php ... +warmed+up
For an example of another good experience with an AFM rebuilt by Fuel Injection Corp., see:
http://fiatspider.com/f08/viewtopic.php ... ction+corp
As seen in the thread linked above, I learned about FIC in May, but the delay in getting the AFM rebuilt was all my fault. The turnaround once you send the device to them is only a couple of days.
Further Addendum:
On 8/25/15, the car's owner and I finally went out for a test drive. She reported that it felt like a completely different car. Running smoother, no fighting to keep the engine from stalling at stop signs, and no "too-rich" odor. Acceleration was good, too. In short, it was finally a pleasure to drive.
I'm comfortable chasing down air leaks and troubleshooting electrical problems. I've done quite a bit of aesthetic, maintenance, and improvement work to the car already, but I have never delved into the interior of any engine - even just as far as the valves. I'm sure checking the clearances is not that big a deal, but it still represents terra incognita for me and therefore causes some hesitation!
So glad to see an end of thread that has resolution 
