Every cycling commuter needs and extra bike, just in the case of emergencies. It would appear that you're already on the right track. However, I would strongly suggest that you convert your fixie into a single speed and allow it to take the roughest Chicago winter days, while the F1X suits your fancy for the remainder of your most blissful days.

PS.

You don't want to wake up late one morning with a flat....Suppose your F1X needs repair at the LBS. That might take several days....

Cycling commuters must always abide by the N+1 rule!