I don't have Direct TV but Dish instead. I doubt if you can just give them a change of address & get the receiver to work the way you want.
Even if you now have the phoneline disconnected .I think they would need to have a phoneline connected to change the programming on the "Smartcard"(Dish's name for it).
I don't have a phoneline connedted to my sat receiver either as I have went all cell & Skype. Dish can add or remove channels & regulary adds monthly "Bonus" channels & then removes them without the phoneline being connected. So they can do some things with the sat signal. I know they regularly turn off my receiver usually in the early morning & then turn it back on.I assume this is some kind of check to see if I'm stealing some channels with a modified "Smartcard". I don't.
Also giving a false address probably violates your contract.
I suggest contacting Direct TV & see if Chicago's channels are available for you.You will probably have to purchase them as an additional package.
I think Dish calls this distant networks or something like that.
When this is done is it your locals the client receives or does the sat receiver continue to receive the LA locals ?