Sounds like you have already rules out a fair number of the possible problems. Not sure of the gas they sell in your location but between the % of alcohol and other blend factors (like we have here in California) the float bowls can dry out rather fast. Being that 99% of the cars on the road today are fuel injected and in a "closed" vent system the evaporative properties of fuel can be much higher.
This doesn't bode well for carburetor cars as it causes the float bowl to dry out quickly. Then you are reliant upon the car cranking, the fuel pump pumping to refill the bowl and the car starting. I dealt with this all the time with other older cars I have. I installed an electric fuel pump near the gas tank to pump fuel to the carburetor BEFORE I attempt to start. It saves a LOT of wear and Tear on the battery and starter.
It is a bit messy, but if you let the car sit a while (for the fuel to evaporate), then using a funnel and hose fill the carburetor before attempting to start it - and it starts promptly you have your answer, evaporating fuel. An electric fuel pump would seem to solve the problem. There are a few things to know about it though:
1. It needs to be mounted low otherwise it can draw air. The pump is better at pushing than pulling fuel. Also, depending on the original pump type I at times need to briefly crank the car to put the pump in a position that fuel can past through when priming with an electrical pump.
2. There is a safety issue. Should the car get in a wreck, or roll over you don't want fuel still pumping. Some people use an oil pressure activated switch so if the engine stalls the pump stops. How they get around the initial starting without oil pressure is a mystery to me. Others use a common Ford shut off switch that is found in the trunk of most Fords. At the very least one should toggle switch on the dash but you are at the mercy of being conscience and able to reach it if needed. So, do all and any at your own risk.
Lastly and not fuel related, most ignition systems take a full 12 volt tap right off the starter when starting, then for the running period go through a resistor to reduce the draw. If for some reason this kit car is not wired properly that might be the problem. This is especially true with points based ignition systems. I have a '88 Turbo Coupe engine in my Pinto and the EFI and computer controlled ignition are very different. Thus I would not be the best person to advise if you have the factory based electronic ignition as I am unfamiliar with it.
I've found that pictures truely are worth a thousand words. If you could post images of your engine/engine bay it might be helpful in getting assistance.