After hearing that the brake switch was faulty, this whole thing makes perfect sense.
After Toyota began having issues with the "sudden acceleration" in the Prius, Nissan began plugging a feature that has been built into their cars since 2005 - the brake override.
To avoid similar Toyota-like issues, in the event the brake and throttle are simultaneously activated, the brake gets precedence and cancels out any throttle input. A faulty electrical signal from the brakes will cause the sensation OP was getting - a stuttering of the throttle in rapid succession. Considering no human short of Slayer's drummer would be able to replicate this with their feet, you wouldn't initially feel that this could be the cause of such.
Glad you got it resolved. Yet another possibility to add to the troubleshooting flow of stutter upon acceleration.
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