Will not start

You listed parts in all different systems, and that will cause different symptoms. That suggests nothing has actually been diagnosed. Replacing random parts is the least effective and most expensive way to solve a problem, as you are finding out.

If the starter cranks the engine like normal, why would you replace the starter or solenoid? Since the fuel pump is working when the engine is cold, it is not a good suspect. It has no idea how hot the engine is. If the neutral safety switch is defective, the starter will not crank the engine. There will be no loud, single clunk from the starter solenoid, just like there is no sound when you do not turn the ignition switch. If the starter works, the neutral safety switch is working.

The most important clues you observed are the need for the engine to cool down before it will start and run, and the starter works normally when the no-start occurs. That combination is an extremely common complaint. The place to start is always by reading and recording the diagnostic fault codes, but understand they never say to replace a part or that one is bad. They only indicate the circuit or system that needs further diagnosis, or the unacceptable operating condition. Next, you need to check for loss of spark and loss of fuel pressure. If only one of those has occurred, that is the system that must be diagnosed. It is much more common to lose both spark and fuel, then you must look for what both systems have in common. That is the crankshaft position sensor and the camshaft position sensor. Both of those commonly fail by becoming heat-sensitive, then they work again after cooling down for about an hour. Sometimes they can have a hard time setting a fault code, but when they do, you will know which circuit to check.

I have a suspicion the mechanic recommended what to replace based on your description of the symptoms, then you replaced those parts. That's hard to determine with intermittent problems, plus, a lot can get lost in translation. This is just as frustrating for mechanics and car owners when you let the mechanic do the repairs, and he never gets to see the intermittent problem act up. It's similar to telling your doctor, "my stomach hurts real bad sometimes, but it feels fine today". He could treat you for any of dozens of ailments, but you wouldn't fault him if the remedy didn't solve the problem. You'd run back multiple times until he hit on the right diagnosis. Mechanics are held to much higher standards. If they don't solve the problem correctly, we assume they're incompetent or out to defraud.

I already explained why some of the parts you listed can't cause this problem. If you explained the symptoms the same way to the mechanic, he should not have been replacing parts in the starter circuit. You need to make the needed observations while the crank / no-start is occurring. That includes checking for spark, which is easy to do, and for injector pulses, which more involved. The parts in the ignition system are less likely to be intermittent, so if you find no spark, I would be willing to simply assume the injectors are also not firing. The clue is you will not smell raw gas at the tail pipe. That leads back to what both systems have in common, which is the crankshaft position sensor and the camshaft position sensor, which on your engine is the pick-up assembly inside the distributor. Both of those often fail when they get hot, then work again after they cool down. The place to start is always by reading the diagnostic fault codes first, but for these two sensors, don't assume anything if there are no codes set related to them. It takes a lot for some of these codes to set. We never approve of throwing random parts at a problem, but in this case, my first suspect is the crankshaft position sensor. Try that first, then if the problem still occurs, head to the distributor pick-up coil.