If you go to Eatzi's and can get them to make you a turkey sandwhich using their house made roasted turkey breast, you will love it! You have to specifically ask for it, or bring some to the deli counter, because other wise they will make it with their deli turkey. They have a make-your-own sandwich bar. They will also grill your sandwich, complimentary, if you take it to their grill (they dont really advertise this)
You can also purchase the turkey breast thick or thin sliced to make your own sandwiches at home on one of their fresh baguettes made in house.
I'd try The Mecca.
http://www.themeccarestaurant.com/ Turkey club on their lunch menu for $7.99.
However, although not a club sandwich, Bolsa Mercado in Oak cliff does a fabulous turkey panini.
Also try The Original Market Diner on Harry Hines Blvd. They're the closest you'll come to an east coast diner in Dallas.