There are several great suggestions here and it sounds like you are doing many of them already - good for you! Have you seen the eviction record on your report? I'm curious because often times old records don't (or shouldn't) show up on a tenant screening report. Many states have laws in place that prohibit screening companies from reporting information that antedates 7 years. This of course is not always the case, and I am not certain of the laws in IL.
I would suggest you ask to see a copy of your report - if your application has been declined you should have been issued a notice of adverse action that explains why you were declined and who to contact for a copy of your FREE report. You can also go to a tenant screening website called MyScreeningReport.com and order your own tenant screening report then share it with multiple landlords at no additional cost for 30 days. The advantage to this is that you can see ahead of time what is on the report that you will be presenting to your prospective landlord. Additionally, doesn't negatively affect your credit score because YOU are the one that is ordering it.
Best of luck to you!