It wasn't just robbing the moisture the convection modulated the mass fields such that the trough never matured properly and the surface low was pulled east. This was never given a chance to properly have the WCB cross into the cold sector because it got deflected east along the river with all the training storms there.
There is going to be a lot more ice than the nam is showing if it's running into as cold of atmosphere that should be in place. Also too the low looks too far north in relation to the 500mb maps. Lastly Nam at this range cut last night's storm through the state only to be spectacularly wrong.
Chicago's area should get lake enhancement which the models are sometimes too coarse to pick up. I wouldn't worry too much I could see most of that metro getting 3-6"
Usually the low tracks south of the snow pack, it's not always but with sliders W-E it does more often than not. Also too the storm Wednesday will leave back some blocked/confluence too, which is why it is more on a W-E path.