1. eink can be made on flexible plastic and be very thin, and cheap too (see http://www.engadget.com/2008/09/08/esquires-e-ink-infused-ma...)
2. charge pumps can be made out of discrete components and the largest part is a coil, which can easily be laid flat and thin. You can also charge a ceramic cap (low self discharge) slowly and use it when you need to change screen contents, thus allowing you to have a smaller charge pump yet
3. PCBs can be made very thin (a cheap pcb fab I use will make 10 PCBs for $10 for me at 0.2mm thickness). And you can also make them on a flexcable that is thinner yet.
You are right about EMV though. It is supposed to be uncloneable.