Carburator

Sounds like you have the wrong base plate gasket. That will create a vacuum leak which will increase engine speed without increasing power, and the loss of vacuum will reduce the effectiveness and strength of the brake power booster. If you use a squirt bottle with water, you will see it get sucked in under the base of the carburetor and engine speed will slow down momentarily.

Just another thought, you might try a carburetor kit, if they still make them. It has been a while since my last carburetor kit. The kit should have all gaskets, instructions and specs. Have you ever taken a carburetor apart?

The only thing would be if there is a third hose attached to the pump. That would be a return line to the tank. If that line is blocked, there is the potential for fuel pressure to go too high and push the needle off the seat in the carburetor. If you look down into the air horn while the engine is running, you will see fuel dribbling in from the accelerator pump nozzles. You could also prove that by pinching off one of the rubber hoses going into or out of the pump.

A little known problem that causes stalling with carburetors, assuming you still have spark, is a plugged pickup screen inside the gas tank. It will collapse, typically after ten to fifteen miles, and restrict the amount of fuel that can get through it. Sometimes you can blow that screen off by removing the supply hose from the pump and blasting it with compressed air. Be sure the gas cap is removed so you do not expand the tank. The symptom of the plugged screen is gradually losing power and you will feel some surging for anywhere from a few seconds to a minute or more. With a little cranking after letting it sit for fifteen minutes, it will run again for another few miles.

If you do find that you have no spark when it stalls, you might suspect the ignition module or the pickup coil inside the distributor. The module tends to fail instantly when warm; no sputtering or gradual loss of power. The wires on the pickup coil flex each time the vacuum advance turns the plate that coil is mounted on. As a potential test, you can disconnect the vacuum hose at the distributor and plug it. If it no longer stalls, it could be because the wires on the pickup coil are not flexing and breaking the circuit. That is not necessarily a conclusive test but it can provide some clues.

Depends what you mean by "shutting off". If the ignition timing is severely retarded, the engine will run too slow and with too little power. That could lead to stalling when you approach a stop sign but it would not cause stalling while you were driving at a steady speed. If you have an intermittent electrical problem, typically that will cause sudden stalling regardless what speed you are driving at. That could be caused by the ignition module, ignition coil, or the pickup coil. Either way, you would have no spark right after it stalled. Check for spark right after it stalls. If it is there, do not crank it any more. Pop the air cleaner off, look down the air horn, and work the throttle by hand. Watch for two nice strong sprays of fuel. If you get none or just a few little dribbles, the carburetor is running out of gas. The symptom will be stalling with a little surging or sputtering before hand, not the sudden stall that electrical problems usually cause.

I am more concerned with the high idle speed indicating a vacuum leak. I misread your first post and was thinking you replaced the carburetor. That is why I suggested the base plate gasket. Instead, look for a vacuum hose that is disconnected or cracked. One large one goes to the power brake booster. Try pinching off those hoses to see if the engine speed comes down.