Perhaps the vacuum valve on the ignition switch is failing?

Start by disconnecting the vacuum line to the shutoff valve. Sounds very much like fuel starvation / filters, have you checked them, the air filter, and the fuel-tank vent & strainer? Does this happen on diesel fuel also?

Try running the car from a tank/jar/can/whatever of fuel under the hood directly into the lift pump to eliminate fuel tank and associated plumbing.

Unlikely that your exhaust cat has become plugged, but it does happen. Pull the plug from the exhaust mainfold to see if that helps.

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Gone to the dark side

- Jeff