I'd have to agree with
juiceman. The fuel pump seems a little suspect to me as well. As far as the MAP/BAP sensor, they act when the car is cold as well. If it was faulty, it would probably show up right away. EGR is the same way. Cold/hot, doesn't matter. The O2 sensors may be causing some problems, but it would have to be really bad to have the car stall out.
Something else to note, the MAP/BAP, O2, EGR, all those will pretty much be negated when the car is floored. Almost all the emissions equipment goes off line. The fuel pump obviously doesn't.
I would bet on fuel pump, or an ignition problem.