The whole assembly is going in to Airflow Performance for overhaul: fuel servo, flow divider with purge valve attached, and 4 injectors.
Okay.
As of yesterday we can put a period on this maddening troubleshooting.
Yesterday we reinstalled the overhauled Airflow Performance FM-200 fuel servo, flow divider, purge valve, and 4 injector nozzles. (I did not send in the injector lines because my testing showed full fuel flow through them.) After we torqued the last fitting and double-checked everything, I dragged it out for a start attempt, having changed nothing else yet except the AFP system.
She started right up on the first compression and ran smoothly up to max ground power. Started on only the LSE electronic ignition, having changed nothing in that system. Then mag check at max ground power was normal on both ignitions, on only the LSE, and on only the Slick mag. Normal-normal. Idle RPM is a bit high at 1050, but that's easily adjusted.
I conclude therefore that it was indeed the Airflow Performance fuel servo that caused my problems. For a month or two prior it had become hard to start on the first start of the day, so something had changed. The reason it finally started to quit on me during landing probably was that mechanical fuel pump also failing, dumping fuel overboard through the external drain line. Unrelated, I think, but that is what finally caused me to start the troubleshooting.
I called Don Rivera at AFP to find out what he did on the overhaul (which incidentally was several hundred dollars more expensive than the estimate.) He said he did not personally do the work, but that it looked like a normal overhaul to him, given the 25-year age of the FM-200. He said the standard overhaul kit was the reason for the higher price: about $410 above the quoted overhaul price-plus-parts estimate! He listed the parts changed. It sounds to me like just about all the guts are new! Including the diaphragms, rod ends, bearings, seats -- the motive parts of the fuel control! It all looks brand-new out of the box. I think all I have left of my original servo is the housing! The injectors, too, look brand new. I think he changed the airbleed screens and shrouds from the parts price and their appearance.
The overhaul was expensive, but apparently necessary. It now starts and runs as it always has: smoothly and immediately, cold or hot.
I'll still change out the Slick non-impulse mag for an E-mag. Get rid of those massive and expensive aircraft plugs, plus the Slick is 'way past its projected service life. I also changed the original LSE coils for their new-style tower coils. I used the LSE adapter plate to just bolt them on in place of the older style coils. Just in case. I couldn't tell any difference after replacing the coils, so those likely were not the problem. But I now have new coils anyway.