I worked as a mechanic as a fleet mechanic 30 years. When a vehicle was towed into our shop with a no start condition the first thing I did was listen to how it sounded while cranking. A broken timing belt or stripped timing gear will effect the compression ratio which changes the sound of the engine when it is cranking, especially if the cam is not turning at all. Often it sounds like an engine cranking that has had the plugs removed. A worn gear that has jumped timing but is still turning the cam might sound normal while cranking but willl not make any attempt to fire, most of the time it will backfire through the carb or exhaust. If the cranking speed and cranking sound seems normal then I move on to the fuel.
Before I checked for spark I would give the engine a squirt of starting fluid, if it momentarily ran on the starting fluid I knew there was a fuel delivery issue. Next, I removed the air cleaner and with the engine not running look down inside the carb and see if your getting a squirt of fuel from the accelerator pump (never look down a carb of a engine that has a starting problem or is running poorly, it’s a good way to loose your eye brows or worse should it backfire back through the carb). Usually if the engine fires on the starting fluid you will not get a squirt of fuel from the accelerator pump. In this situation 90% of the time you have a bad fuel pump. If its an electric pump, with the pump energized, if you tap on it with a hammer it will usually start pumping, most of the time this will get you home along as you keep the pump running and don’t shut the engine off. A plugged fuel filter will usually allow an engine to start and idle fine but it will act like it is running out of gas as you try to accelerate. Sometimes a carb’s needle and seat will stick closed from sitting for a long time, usually a slight tap on the carb above the seat will un-stick them. Since you have two carbs if one was bad it should still try and start on the other one. I don't think you have a fuel problem since the plugs are fouled and the crankcase is filling up from fuel from the excessive cranking (do not crank an engine for more than 15 seconds because the starter will over heat, allow 15 seconds for the motor cool down between cranking) With a fresh set of plugs even if it was flooding over it should start and then gradually run bad until the plugs become fouled and it stalls. If your plugs are fouled they need to be cleaned, it is not going to start with out a fresh set of plugs. I bead blast fouled plugs but you have to be careful to get all of the sand out that gets wedged down inside of them.
Next I would check for spark. With an electronic module you can damage the module by holding the plug wire too far away from the engine. If the distance is too far for the spark too jump it can backtrack through the distributor to the module and damage it, you may not notice the damage right away buy eventually the module will fail. The best way to check electronic ignitions is with a special spark plug tester which is basically a plug with an alligator clip on it. This little inexpensive tool will also keep you from getting the crap shocked out of you. Do not leave plug wires loose on an electronic ignition while cranking the engine unless you disable the coil. You mentioned you had pulled a plug wire and you have spark, you should have a nice strong spark, if it is too weak it may not fire the mixture. Getting a good blue spark can be deceiving, just because you have spark does not mean its happening at the right time. I have seen electronic control modules malfunction where they will still make plenty of spark but they loose their ability to control the firing order. That is why on and engine that will not start but has good spark and fuel it is a good idea to check the timing while cranking the engine to make sure the module has not developed some form of Alzheimer’s. You said you replaced the module and you have spark so your ignition system is probably ok.
It sounds like you have checked the basics. My gut feeling is you have a timing problem but since the early flatheads do not have a timing mark you cannot check it with a timing light. If it had a mark you could have someone crank it while you check it with a timing light. Like V8 Bob said the crab distributors only go on one way because the keyway is offset to one side, it was a really neat design. I'm thinking that the fiber cam timing gear sheared some teeth off of it, it could have even broke a cam, if it did you will have a compression problem, a valve timing problem and an ignition timing problem. You could try and pull the distributor cap and turn the engine back and forth in several different positions and see if you have excessive play in the rotor. Even though you have spark it could be that the gear is just occasionally catching and turning the distributor. Crank the engine and see if the igntion rotor turns. You can also do a compression test. You could also drain the oil and see if any timing gear fibers come out.
Your probably wondering why a cam gear would run around town and then die after it gets back home. I’m not sure why this happens but we used to have a bunch of 460 Ford engines in out fleet with nylon timing chain gears, around 60,000 miles the cam gears would fail. Typically a guy would drive around all day and make it back to his parking stall but the next day the truck would not start, I would pull the distributer cap and the rotor would not turn while cranking the engine. I saw this happen several times. I’m guessing that the little extra exertion on the cam gear teeth to get the cam initially turning shears off the last remnants of the teeth, maybe with a cold engine it takes a little more effort to rotate the cam?
