I actually moved down here from downstate - the Quincy / Springfield area - about six years ago. I used to travel to Chicago regularly for business and pleasure. My girlfriend just moved down from the northwest 'burbs about two and a half years ago. She's from the Rolling Meadows / Arlington Heights area. She's a Cubs and especially a Blackhawks fan. I'm a Cards, Chiefs, and Blackhawks fan.
There's a Gino's East up around Spring / The Woodlands. Groupon has a $30 for $16 deal for it right now. It's not quite the same, but it's much closer than anyone else down here. There are some other decent deep dish places, but most of them don't get the cheese/crust layer just right and don't use any corn meal in the crust.
I work with some Chicago transplants, too. I can probably ask around about whether anyone's found something close to Giordano's.