Continental Airline Tickets

What's my best option for a late arrival into Midway Airport in Chicago for ground transportation? I have a flight that lands at midnight, and the only airport shuttle (Continental Airport Express) stops all pickups at midnight (per their phone representative). I do know that there is excellent public rail (CTA) transport into downtown. However, I am *VERY* reluctant about arriving in the wee hours of the morning, catching hauling our luggage into a CTA train, then getting out to change trains once, then hauling the luggage to the street and walking several blocks dragging luggage around. If it was the middle of the day, I'd feel OK about it, but not at that hour of the night. Also, I'd rather avoid getting into an expensive cab ride unless there was absolutely no choice. What company can you people recommend that would still pick us up at, say, 12:30 am, and deliver us to the miracle mile? thanks!