You've done most of what I would suggest and from my experience causes similar symptoms. Other possibilities are bad plug wires, a loose plug wire or a bad ignition module. Possibly a bad cam PS but that usually throws a code.

Dying while pressing the accelerator is in my experience a symptom of poor ignition (which floods the engine) or too rich a mix (which floods the engine ). But right now there isn't any way that I can tell which is causing the problem. You may even have more than one problem causing this.

Since there can be so many causes to this I would take the vehicle to a shop with a good engine monitoring system that will record multiple sensor readings and try and duplicate the problem with them monitoring it. Be prepared to pay a couple of hours labor for this.