That Kennedy is not a doubled die. It is double struck. Reason I say is because the profile of the letters at the field are the same thickness that they should be with a normal die, and the split takes place at the high point of a normal letter - typical double struck. A doubled die would have thicker letters, not just split letters. It is the lighting that gives it the pronounced split appearance.
Sean, this could be the reason for the E being smaller:
The next step is to reduce the design on the galvano to the actual size of the coin to be produced. To accomplish this, the Mint uses a Janvier Transfer Reducing Machine. This machine, operating on the principle of a fulcrum, will trace the design on the galvano. This is accomplished by a long metal arm with a tracing stylus on one end as the galvano rotates. The tracing will be transferred to the opposite end, where a sharp cutting tool is positioned. This cutting tool will be carving the design exactly as it is traced from the galvano onto the end of a steel bar. This steel bar will usually be about 2 inches in diameter, and tapered so that the end being cut will be the actual size of the coin to be produced. The steel bar will also be rotating, however at a slower speed, so that the design being traced from the galvano will be properly transferred. The process will usually be duplicated at least once to ensure proper sharpness of the design. Once complete, the steel bar will become what is known as the master hub (sometimes called "hob"), with the design again in relief, as it will appear on the finished coin.
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The next step is to reduce the design on the galvano to the actual size of the coin to be produced. To accomplish this, the Mint uses a Janvier Transfer Reducing Machine. This machine, operating on the principle of a fulcrum, will trace the design on the galvano. This is accomplished by a long metal arm with a tracing stylus on one end as the galvano rotates. The tracing will be transferred to the opposite end, where a sharp cutting tool is positioned. This cutting tool will be carving the design exactly as it is traced from the galvano onto the end of a steel bar. This steel bar will usually be about 2 inches in diameter, and tapered so that the end being cut will be the actual size of the coin to be produced. The steel bar will also be rotating, however at a slower speed, so that the design being traced from the galvano will be properly transferred. The process will usually be duplicated at least once to ensure proper sharpness of the design. Once complete, the steel bar will become what is known as the master hub (sometimes called "hob"), with the design again in relief, as it will appear on the finished coin.