Hot starting issues

When your ECU sends ONE spark during the shut-down, this proves that your entire ignition system is working; except the magnetic trigger, you have to test that separately.

Since you have already stated that your system is doing this, when hot, you can safely assume that your coil, ECU, ballast, and ignition switch are all working properly.
So to me this is an easy diagnoses; the next time it craps out, pull the coil wire out of the DISTRIBUTOR and near-ground it about .25 inch . Then crank the engine. If everything is working right, there will be a stream of sparks issuing from the wire. and you can move on.
If no spark-stream is visible, check the the case-ground of your ECU. If that is good, AND your ECU still passes the ONE-spark test at shut-down, AND your Ballast resistor is known to be good, then go after the pick-up and or reluctor-gap.
In my experience, the reluctor gap works from ZERO gap to .030, but the spec is .008 to .011.
The pick-up has a resistance spec of something like 300 to 400 ohms depending on it's temperature, but I have measured good working ones as high as 900 ohms. And I have measured non-working ones at 350 ohms.
My pick-up test is this;
I pull the still-connected D out of the engine, and with the Ignition in "run", I spin the driveshaft. A stream of sparks should issue from the near-grounded coil wire.
The thing with the pick-up is this;
the wires are multi-stranded something like 11 of them each, and the constant flexing of the reluctor-plate by the Vacuum advance tends to break them over time. Even just one connecting wire will still measure a Correct resistance..... but that one wire may not provide enough signal for the ECU. So I go to the manual-test as above.
Besides, it's so much fun to spin that shaft and see the spark-stream..... lol.