Answer: You could buy a new car, but I suspect that you would prefer to solve the problem on this car. One of the things that I enjoy most about classic cars is that they are relatively simple and therefore generally easy to troubleshoot. However, sometimes common sense and past experiences are actually a hindrance when it comes to troubleshooting a 1958 car in 2011.
Let me explain. The symptom that you are describing is actually quite common. The only thing that stands out in your case it that it occurs on a daily basis, whereas it is much more common to see it when a car sits for a week or longer. Because it is a common problem, we look to past experience for the remedy, just as you did, and you replaced the suspected parts.
However, in your case, I believe that the cause of the problem is completely different, and that is where the year 2011 comes in. Because of additives in modern fuel such as ethanol and alcohol, the fuel evaporates at a much lower temperature, and therefore much faster than the fuel that was available when your car was built. Back then the fuel could sit in the carburetor bowl for weeks, or even longer, without evaporating enough to cause problems. Not so today.
The only solution that I’m aware of is to replace the mechanical fuel pump with an electric fuel pump and regulator. This is a very common and easy installation. Do not leave your mechanical fuel pump in place. Remove it and replace it with a “block-off plate.” You will be amazed at how easily your car will now start.
If commitment to originality precludes you from using an electric fuel pump, you will need to either prime the carburetor with gasoline on a daily basis, or utilize a starting procedure that will minimize wear and tear on the starter. The best way to do this is to crank the engine for about 10 seconds without pumping the gas pedal. Then pump the gas pedal a few times and crank the engine again. If gasoline has been pumped to the carburetor, the engine will start right away. If it does not start, repeat the same procedure. As soon as gasoline reaches the carburetor, it will fire right up.
One more thing…have you checked to make sure that your choke is functioning properly?