Your only other bet, and maybe not much better, is to build a custom connection through MCO. Not sure of your dates, but looking in early March and you can depart MDW at 5:35am and get to IAD at 12:30pm thru MCO. A little over 4.5 hours of flying time plus the 1 hour layover in MCO. Just beware of the usual caveats of a custom connection (combined fare maybe higher/lower, no protection for IRROPs, checked baggage potentially not making it all the way). Obviously, going N/S out of ORD on UA makes the most sense but this may be an option if you must go out of MDW and/or use WN.