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I have the exact same problem on my 68 Dart with a Holley DP carb. One day with the hood and air cleaner off I saw what the problem was. When I braked hard, I saw gas was sloshing up through the vent tube, which was flooding the engine out (unless the idle was kept up). I have since heard of other people experiencing the same problem.

Fuel sloshing out the vent and down into the venturis can be cured with a 'vent extension tube'. It fits on the inside of the top of the fuel bowl and acts as a 'baffle' for the vent. Don't have a pic but it is a flat, black plastic tube about 1.5 inches long. This is different than the jet extenders which prevent the jets from being uncovered.