I have made some progess, but I'm still not quite satisfied.
The cold start problem was easy. The thermo-time switch in the coolant manifold wasn't working (always open). Rather than spend $110 for a new one, I simply bypassed it by splicing into the harness and grounding the green wire which is the low side of the injector. Since the high side of the injector is powered by the starting circuit, the injector now squirts whenever the starter is cranking. Doesn't seem to have caused any problems. This trick probably won't work on 3S-GE and 3S-GTE engines whereby the ECU senses the green wire (it'll think the engine is always cold), but on the 3S-FE this terminal is used soley to fire the injector, and the ECU only senses cranking voltage.
As to the ignition, I ended up replacing the ECU with one I got off ebay. The new ECU did change the character of the ignition advance somewhat, although at 10 BTDC is still pinged a bit. I found that with the timing set to 7 BTDC the engine is driveable, and pings only very occasionally.
Have I mentioned how much I miss carbeurators and mechanical advance distributors?
One thing I discovered along the way, which might be helpful to others, is that it is impossible to accurately test an AFM with just an ohmmeter. The resistance jumps all over the place.
What you have to do is test the AFM with a voltmeter while it's hooked up to the car. Turn the key on (engine not running), and measure the voltage between terminal VS and ground. A working AFM will produce a smooth, linear transition between 0.5VDC and 4.5VDC (or thereabouts) as you open and close the flapper by hand. It helps to have the AFM uncoupled from the air box and hose, with just the wiring harness plugged in. It's also difficult to get to terminal VS without cutting the caulk and opening the AFM, since the body of the connector is sealed by a rubber boot. In my case, I already had it open.
Now, we move on to the transmission, which grinds into second when warm. Anybody ever try using GL-5 instead of ATF on an S53 5 speed?