Had a similar problem caused by a wire leading to the module where the conductor was broken inside the insulation. Car ran fine until you stepped on it pretty hard and then it just died,letting up on the gas would get it running again. Where yours will start after you've removed the cap could point to a similar problem since you kinda rearrange the wires when you remove and replace the cap. It would be one of the wires that leads from the cap to the module. Those wires are flexed when the distributor moves during vacuum advance and also every time you remove and replace the cap. Good Luck!
Ron