No doubt about it...bush honeysuckle is a scourge of forest management in Illinois forests.
I'm willing to bet that you can't find an experienced professional forester or wildlife biologist who will argue for keeping bush honeysuckle in your forest.
To assist you in your endeavor, might I suggest you develop a forest management plan approved by the Illinois Dept. of Natural Resources (DNR). Contact your local DNR forester for a list of professional consulting foresters in your area. Moreover, this DNR approved forest management plan will open the door to federal and state cost-share dollars to help you eradicate this harmful exotic from your woodland. The federal Environmental Quality Incentives Program in Illinois has a brand new suite of forestry cost-share dollars and programs. Contact your local DNR forester and local USDA Natural Resources Conservation Service office for more information.
Some native small trees/shrubs to consider include eastern redbud; dogwood spp.; viburnum spp.; witch-hazel; hazelnut; Amelanchier spp.; sumac spp., etc. There are others, of course, but I suggest you work with a local professional to match stand conditions and soils if you are to plant a significant amount of trees/shrubs.
Best of luck!