The car in question (1929 Packard) has a vented float bowl so boiling fuel in the carburetor may not pressurize the bowl. The vent is a small hole in a screwed cap, I removed the cap on my cars providing a bigger vent opening, that made no difference
In my opinion the problem is simply that the fuel drawn into the engine is a mixture of liquid and vapor. The vapor has negligible energy so the car starts "bucking", as the vapor part starves the engine of fuel. Pulling out the choke or full throttle can provide slight improvement but once it starts, stopping and cooling the vacuum tank and carburetor with a wet rag will provide temporary relief.
The problem is as simple as that, the cure however is far from simple, how to keep the fuel cool.
It's worth adding that on later model cars vapor lock might be due to the fuel pump not delivering vaporized fuel, pumps deliver liquid not vapor. On cars with a vacuum tank, its not a pump, its simply a tank under negative pressure (when the float drops) and as such will suck liquid or vapor if required.
A final comment despite this being a real PITA when it happens, sometimes a year or two will pass without a vapor lock incident occurring leading to the belief that the latest "fix" has somehow been the cure, then when conditions are "right" it happens again

In discussions with a fuel company (BP) I was told there is no relationship between octane rating and fuel volatility. What you may find is that the higher octane fuel does not have ethanol

I had two 1929 Packards, on one I re-ran the fuel line down the opposite side for the reasons described, it made no difference. There is very little heating of the fuel in the line from the fuel tank to the vacuum tank. The problem starts with the fuel stored in the vacuum tank located in a very hot engine bay and above the exhaust manifold.

When you say that priming the vacuum tank didn't work, do you mean it started but still had no vacuum or it would not start? If it started then there is inlet manifold suction so the problem is between the manifold and the vacuum tank. The suction at the pipe where it connects to the vacuum tank when the engine is running is strong, is the piping blocked?

The Packard company issued this letter to its dealers in 1931 giving instructions about modifications to avoid vapor lock. It states that the fuel had become more susceptible to vapor lock. The fuel today is far more "susceptible to vapor lock" than it was in 1931. The problem is that it vaporizes or boils at a much lower temperature. It is certainly not a new problem

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The fact that your pump feeds directly to the carburetor is interesting. That should overcome most vapor lock events. If you are using fuel with ethanol that could explain the problem. I found it made the problem much worse.

I would add a few cup fulls of fuel to the vacuum tank to get the car started to see if it pulls vacuum when the engine is running.

I missed the point that your vacuum tank does not work. Does your electric pump bypass it? If not it should however I would recommend you fix the vacuum tank. The electric pump should only be switched on to overcome vapor lock otherwise it can overcome the carburetor cut off and flood the carburetor. Much has been written about that.
Your experiences with opening the hood are exactly the same as mine. Also when I parked my cars in summer I always left the hood open otherwise the car would be hard or impossible to start unless they had hours to cool down.
Someone mentioned diesel instead of kerosene. I tried it once on a long trip in hot weather when the car was constantly vapor locking, I can't remember the % added but it was a lot. It made no difference good or bad.
On that trip I improvised a way of holding the hood sides up a couple of inches while driving. The increased airflow into the engine area significantly reduced the problem. Later in the day a cool change occurred and the vapor lock problem instantly stopped. I have driven one of my 1929's in light snow and it never ran better.
Another time I had to drive when it was just over 100 deg. I constantly had to stop to wet the carburetor and vacuum tank to cool them. That provided instant but very short relief.
I should add most of the time my 1929's were great cars to drive. I drove the 633 Roadster on many long-distance tours over twenty years. It did not have an electric fuel pump, only the vacuum tank. The other car was a 633 Sedan and I fitted it with an electric pump bypassing the vacuum tank. So when it vapor locked I switched on the pump giving almost instantaneous relief most of the time. On very hot days nothing much works. Stay home or stop and wait for the sun to go down!

I would assume that your 1929 Packard is in good running order under all normal conditions, as were my two 1929 Packards. Mine started, idled and ran well under all conditions except when it was particularly hot weather and then they sometimes vapor locked.
Vapor lock does not happen all the time, only under adverse conditions. When it happens the engine will run for a second then starve for fuel for a second and keep doing that until it either corrects itself or the engine stalls. It might happen on a long steep climb and be fine when it is back on the flat and not working so hard. It might happen in stop start conditions when there is less air flow through the radiator. It never happens in cool or cold weather.
The problem is caused by the fuel in the carburetor boiling. When that happens the fuel drawn into the engine is intermittently either normal atomised liquid or vapor from the boiling fuel. The vapor has little energy so the engine starves and misses.
The problem starts in the vacuum tank where the fuel is heated by its proximity over the exhaust manifold and from engine bay heat. The fuel will boil in the vacuum tank. I have proved this by removing the top when it has happened on my car. Even though it is boiling it flows under gravity to the carburetor where it continues to boil. The boiling fuel is drawn through the carburetor to the engine as a mixture of liquid and vapor which is what causes the erratic running. There is negligible energy in the vapor so the engine starves for fuel.
Fixing the problem is not entirely possible under worst case conditions. Everything possible must be done to reduce the temperature of the fuel and that is far from easy. A heat shield under the vacuum tank is essential. An electric pump bypassing the vacuum tank is probably the best solution as there will be far less fuel exposed to the very high engine bay temperatures so it will be cooler when it reaches the carburetor. An electric pump feeding the vacuum tank does nothing to solve the problem. Getting the fuel to the vacuum tank is not the problem.
Another solution is to raise the temperature of the boiling point of the fuel. The fuel does not have a single boiling point like water, it is a mixture with many different boiling points, the lowest being around ambient temperature on a hot day. Mixing kerosene with the fuel raises the average boiling point of the fuel mixture, it dies not change the boiling points of the fuel components, it simply provides more higher boiling point fuel. I have spoken to fuel companies who have confirmed its effectiveness and that it is not detrimental to the engine. However the fuel needs to have at least 10% kerosene to make any difference, 20% is better. Such quantities can be difficult to obtain.
Another solution, although hardly practical, is use Avgas, available at airports. Avgas has a much higher average boiling point for obvious reasons.
These comments only apply to the models with vacuum tanks for fuel delivery. The problem may be different on cars with mechanical fuel pumps,

Kerosene added to the fuel works better than diesel. Add as much as you can get with a minimum of 10%. Also avoid fuel with ethanol.
I have had two 1929 Packards and both suffered vapor lock in hot weather especially stop-start driving and hill climbing.
When all else fails, carry a bottle of water to wet and cool the carburetor, this gives almost instantaneous relief but only for a very short time.
A fuel circulation system with a return line to the tank can work but the return line flow has to be regulated to prevent starving the carburetor under high fuel demand.
There is no easy fix.

You need to unscrew it anticlockwise a small amount to disengage it. It can be difficult to engage the shallow hexagonal indent on the cover without a suitable tool.