Does the car have a ported vacuum switch in the thermostat? If so, is it opening up a vacuum leak when it reaches temperature?
May want to check/replace the fuel filter sock in the tank. Those YF carbs are bad about the base getting loose and creating a vacuum leak. RBS is a better carburetor in my opinion.
Maybe some six years ago, I had the sending unit rebuilt along with having the mesh sock replaced. In a couple of weeks, when I can spare the money, I’ll get a rebuilt Motorcraft alternator. I don’t know if that will fix the stalling, but I do know the existing one is under-powered. After I do that, I’ll report back here how the engine is. Thank you for your suggestion!
Without making actual tests, it's possible to throw parts till you've bankrupted yourself and still not have fixed it. I'm bettin' the alternator won't fix it, at least you'll have a shiny lump to look at when engine is stalled. Test to see if there is enough voltage at the ignitor. Rather than actual voltage reading, Pertronix describes using a jumper wire, crude but effective. Definitely should measure coil resistance.
I can check for ohm’s resistance in the coil. The engine only starts to run rough at about 3 1/2 minutes. Would a faulty coil let the engine run well for the first three minutes, then diminish?
As far as my experience, coil failure is blown far out of proportion. I've never had one totally fail. The Pertronix unit in my Cobra did cause the original coil to leak but still works fine. I no longer use it but last time I tried on another system was OK. Ignitor I does not have dwell control, current limiting is performed by resistor in coil circuit. Ignitor I connected directly to 12v will draw excessive current. Coils for Ignitor II or III system should not be used in a I system. Try this, before next cold start, turn on switch for a couple minutes. Then start. This will allow the Ignitor & coil to begin warm up. If problem is electrical/heat related, that should shorten time before problem appears. Use caution, Pertronix says allowing switch to be on for a extended amount of time can damage Ignitor and/or coil. You should still measure coil resistance, for Ignitor I, less than 1.5 ohm is too low. Be sure to zero your meter, often leads can read a ohm or more. In that case, one ohm in leads will add to measured coil resistance.