The Illinois gerrymander isn't really all that strong. The main purpose of it is the two swing seats in the south (which Republicans currently hold both...).
What else is there? The 3rd or 17th?? Possibly, but really I doubt it'd change much with an independent commission. It's not like they'd create a Republican gerrymander and eliminate those area's Dem voters.
The Ohio map has a lot more to go after, you can make four Dem seats in the Northeast that aren't that crazy looking, a Toledo seat, a Cinninatti seat. Maybe a competitive Dayton seat. It certainly wouldn't be a 12-4 map anymore.
The most likely neutral CD map in OH is 9-7 or 10-6 Pub, but it can go to 8-8 if competitiveness is pushed as a criteria. The Pub skew is due to the requirement of a black district in NE OH. So it represents a shift of 2 or 3 seats from the current map.
Keep in mind that the Dems gambled and lost on a 13-5 map, but a safe 12-6 could have been drawn instead. A neutral 10-8 Dem map represents a 2 seat shift from what they should have drawn and does balance OH.
In any case the most effective gerrymanders are at the state legislative level and that's what the amendments would address.