Both of those are posted no md'ing. State parks meeting criteria designated by the state archaeologist are completely off limits with rangers there on the lookout for it. Other state parks do allow detecting, you need to check in at the office of each one for the permit, where available and for further restrictions.
Most restrictions involve use of digging tools, site-specific info such as where in the park md'ing is allowed, etc..
Some state parks have rangers on site that are still rather casual and informal but those are few.
best thing to do is just ask farmers if you can go on their property around the parks. Remember they had to get to the area somehow, meaning they could of past right by a spot out of state park lines you know
I believe there were three strong houses (small pallisade forts) along the south side of the Illinois River within an hour or less of Ottawa that are now in farmland. These would not have seen much use as intended, but still may hold extraordinary relic-hunt value.
You will have to pour through old records to find the one or two of these which are not widely known but the one I found had nothing to offer as permission was not granted to hunt the field. These were up on the plain along the old highway runniing along the river path, between the canal land and the river and were not large, but rather intended for short-term usage.
Illini may be off limits too. You'd have to go there and talk to the site supers to get details. If it contains anything considered historical it's now off limits.