Engine runs good but stops after a short while

It would be most unusual if both carbs suffered the same blockage at the same time and applying the cold start would tend to compensate for many types of blockage and produce some sort of firing up and running albeit poor.
Are you sure the fuel is good and hasn't been contaminated in some way? It doesn't need very much water to stop an engine and there is other stuff that can deliberately put in the tank...

That leaves spark or some sort of mechanical problem - you say there is spark but is it good enough?
Is the engine compression good?

It pays to check and test systematically instead of throwing new parts at a problem - a new spark plug doesn't guarantee a good spark any more than a new carb guarantees fuel is reaching the cylinder...
An engine to start and run needs: -

Compression.
A good cranking speed.
The right amount of fuel being delivered into the cylinder.
A good spark.
Everything happening at the right time.

At least one of those things is absent and we can't help you discover which...

Check gaskets / seals / piston rings as it sounds like oil contamination is fouling the plugs.

First you must determine if the fuel is stopping or the spark is stopping..If the fuel is stopping this could be a computer problem.. If the spark is stopping then it could be the IGN Module in the distributer. or any nomber of sensors. Squirt a little fuel directly into the Throttle body on the intake manifold.. If the truck runs longer its probably loss of fuel.. Do this several times to make sure, be careful and only use a small amounty of fuel.. you do not want a fire.. RE: Spark: Take a plug wire and an old plug..put the wire on the plug.. hold the plug against a good ground .. have someone crank the engine .. does the plug stop firing? The engine dies.. and will not restart for a minuet or so.. during this "no start" time do the plug test. If the plug will not fire during this time take the module out and take it to Orillys Auto parts.. They can test it.. really expensive part. Don't replace until you know it is BAD..

If it has an automatic choke, this will keep it revving more when the engine is cold and less when hot. Maybe adjust the idle setting screw on the carburettor so it revs slightly more. Try that before it is running hot. Only increase the revving gradually to the stage where stalling would be avoided when hot. Gradually so that there is not too much revving when cold. Adjusting and testing over a few runs could be a good strategy

check fuel pump pressure- fuel filter --air filter --egr valve if carboned up clean or replace and cat converter feel the exhaust if feels restricted may be clogging up

Have you checked the spark plug? Mine was doing the same thing. Not staying cranked and sputtering while running. I changed the plug and it runs like new. Hope this helps

I had 2 experiences like that. 72 ford pickup I was watching it try to run after I got home from work. It was dark and I could see sparks. I also noticed the coil was very hot. I changed to coil and all was well. I had a 94 sunbird it ran good at high speeds but I could not keep it running at a stop sign or stop light. I change the plug wires. I had not code. I suggest you check the code if you have a check engine/warning light. It can help narrow your search.
I don't even remember if the 72 had codes back then but I have learned to check them any time I have a check engine light.

sounds like you need to have fuel pressure test and check for plugged fuel filter

sounds like a bent push rod or bad starter