I would cut back the old browned foliage now. Cut it down to about 4-6 inches. When you start to see some new growth, then I would dig them up and move them. Make sure to water them to get them established and take as big as root ball as you can so as to lessen the shock on the grass. Being that these are only two years old should make it a fairly easy move. User a wheelbarrow if you can to move it without killing yourself and grab plenty of help. You'll find these buggers are pretty tough and can take almost anything. I moved two last year and they preformed all summer long without a hitch.
Good luck !!!

Blackie