Techincal check: Are you back to a regular computer yet? 
if so, use the Search box above this thread, and look for:
AMEX 3X CLI
AMEX Backdating
for lots of commentary / discussion about same.
Wait until January to app for the BCE. As noted, your new card will have January 2014 as the "Member Since" date, so instantly a year old card.
Do not do the CLI on the other cards if you intend to close them. There are certain aging restrictions on the credit lines before AMEX allows you to move them around. For example, the source CL you are transfering out must be 13 statements old, if I'm not mistaken. The May 2013 card is already on a clock. If you CLI that ED card, I think it has restrictions on how you can move that CL around. Also, once you run the CLI on ANY of your AMEX cards, ALL other AMEX cards must wait 6 months before ANY can get another auto CLI. Strategy and timing are everything in your case. Since you already CLI the ED card, when does that 6 months end?
With the BCE, you'll start with whatever credit line they give you. After 61 days you can do a 3X CLI request (detailed elsewhere, and at least 6 months after the ED CLI) and then when the other cards reach a certain point, probably move the CL into the BCE.
Good luck! You might want to make a chart with all the possibilities. Then you can add it here and we can all comment 
