with my experience, the combo of Admin/Mime is best done at the begining of the game. At that point, the opponent won't typically take just a few cards, because that would mess with their set-up. Of course, they would stay just a few cards shy of the KO, but that is just the start of the game (you have to think about what you are going to be doing for the long game).
Late game, I usually don't do the Admin/Mime combo, and Admin is just there to refresh my hand.
Just so everyone knows, the deck doesn't revolve around Mime; Mime is just a really nice convenience and a sneak attacker/ back up in the late game.
After worlds (where I am ASSUMING that they will drop everything up to and including Deoxys) I think that the best way to go with this deck is to make it a pure Espeon ex and Mew Ex ( 3 of the old, and 1 of the new) and maybe some other supporter running through there, but I'm not too worried about after worlds.
One last thing... the mimes aren't really working at all, other than for the beginning combo. Maybe it's because of the person (that's right, there is only one other person that I play against with this deck now) that I play against, but I would really like to see someone else try this out and give me some feedback. Thanks!