340 Starting issue

Don't throw parts at it is my suggestion. Do test to rule things out.

Fuel from pump to tank. Get a fuel can with some fresh gas in it, disconnect feed side at pump and hook up a loose hose, stick other end in the jug. Start it up. Did it fix it? No, that part of the system isn't your likely issue.

I've had cars where the wires at the coil were loose. Car runs for a little time, but, slow sputters and dies. Check those connections.

Test one thing at a time. Starts and dies, fuel, loss of ignition (coil/bulkhead/igh1 and ign2 wires). A test light is really useful for ignition testing. Positive side of the coil, does it stay on at all times?

Just have to attack it systematically.

Good that you got it running...