Thank you all! Your conclusions have pretty much been in line with what I was thinking -- specifically that:
1) It's perfectly legal. In much the same way as openly carrying an AR-15 up and down the streets of Houston.
2) Chicagoland clearly has no issue with making up their own rules as thing go along.
3) You'll beat the rap, but there's a better than slight chance of taking the ride
4) Flying INTO Chicago wouldn't be an issue. Flying OUT of Chicago is another story.
I've decided that we will not fly into Chicago. Even though it'll cost us about $400 more to go elsewhere, I'm putting my money where my mouth is. I don't patronize 30.06 establishments, and I won't financially support the Chicagoland quagmire either.
Last night, after posting my question, I went ahead and called the Chicago PD. I had a very pleasant and constructive conversation with the duty sergeant. Although he was clearly in our corner in that FOPA would apply, and a Texas CHL would suffice for an FOID substitute, he was clear that showing up at the ticket counter to declare a firearm COULD generate a "man with a gun call," and that if I encountered the Chicago PD in that instance, I would be arrested for bringing a firearm onto airport property. He did say that it was probably legal, but that the courts, not the beat cops, would be the ones to sort it out.
I was expecting a holier-than-thou OMG what do you think you need a gun for attitude, but it was quite the opposite. He made his contempt for the current system and mindset very clear, and mentioned that they were expecting to see changes around those internal policies by the end of the year--but that for now, I'd be best off to consider O'Hare off limits . . . and that coming INTO O'Hare would be no problem at all.
So, to conclude, I'll go elsewhere, and consider my contact with Chicago PD a "good contact" even though I don't like the answer...especially given that they don't like it either.