Joe's suggestion regarding two antenna systems is the one most likely to work best but will come with a level of either expense or inconvenience that may make that option less desirable to many users.
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Why not just remove the reflectors and get both directions since Chicago is 168 south and Milwaukee 353 north? This almost 180 degrees opposite.
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I've recommended that option for your area for years for the UHF stations with very good results.
For locations that are nearly opposite each other and there are no co-channel conflicts, I've advocated for the choice of the bidirectional reflector-less option versus the "combined-two-antenna" configuration for quite some time. Barring potential multi-path concerns, it simply works better. It offers higher net gain by around 3 dB which improves system noise figure and completely avoids the pitfalls of trying to combine two antennas by avoiding phase cancellation. It also costs less than half of the two antenna option.
The two-antenna option combined via a reversed splitter suffers a theoretical 6 dB hit in gain over the gain of the individual antennas. A reflector-less version of one of those same antennas only experiences a reduction of up to 3 dB of the gain of the unmodified antenna in its primary lobe.
This is a not a one-size-fits-all proposition, though. There are times when the two-antenna option is the better choice.