Ride Oswego! It's dry most of the time
Actually, there is one singletrack option available when Palos is wet - Saw Wee Kee in Oswego (way west/southwest of Chicago). The place has a lot of sand (not beach-like, just higher sand composition in the soil) so it drains far better than most places. Last weekend, I rode when it was 28 degrees and it got to 36 degrees by the time I was done. Trails were dry and beautiful the whole time. Palos, on that day, was turning to mush when the temps got over freezing. The guys in the new CAMBR Oswego chapter told me how the place practically never has puddles and so far I haven't proven them wrong!
It's a lot smaller than Palos, but for being a quarry once (long long time ago) it boasts a rippling topology. The singletrack there has very few straight lines.
And because I know the CAMBR Oswego Prez will want it said: The CAMBR/Oswego Park District partnership is new and fragile. If people race down the neighborhood streets to get there or piss off other trail users, word will get back to the park staff that we're not the kind of people who should be allowed there. If things go well, CAMBR will be allowed to improve the place and put up decent wayfinder signage.
So... ride it and love it.