Have you consulted an architect? I'm a Wicker Park resident and the majority of garages have no way of getting to the alley other than opening the garage door itself. Plenty of new construction uses the full width of the lot (standard 25ft wide) to build a 3 car garage for a 3 flat. I can't see why you would be required to build a door into the garage door to obtain a permit as I've never seen it in the city. I don't know all the details but to me it doesn't seem necessary based on what I see on a daily basis. I'd like to know more.
Best of luck, Ken.
It appears you are indicating that you would not have room for a 3 car garage door and the required "Man Door" or gate. This sounds like a pretty straight forward problem for an Architect. A local Architect should be able to advise you on the local code, and design a carport and entry system for you and your cars as required by the city.
I am making an assumption that you have a 25 ft wide lot. You probably need 7 feet per car. which leaves you only 3 feet. Since the "Posts" you mentioned take some space, you do not have the room for all the things you need across the back. So you're thinking, how can I design a door that will satisfy the requirements of the city, and get me the three parking spaces for the cars. Right?
The problem you will have with your creative idea of incorporating a "man door" into a "garage door" is that if there is 3 cars parked, there is no unobstructed egress from the back yard to what I assume is an alley.
How do you get out and the firemen get in? How does the garbage get collected? Are your garbage bins stored and removed from this area? How do you handle this now with three cars parked? Do you have to move a car, or do you just make it all fit because you are not obstructed?
This is an interesting question and maybe there is a solution out there that will allow you all the things you need. How about an elevator? Really! I think talking to an Architect is your best bet.